You are given an array a of n integers, and another integer k such that 2k ≤ n.

You have to perform exactly k operations with this array. In one operation, you have to choose two elements of the array (let them be a_i and a_j; they can be equal or different, but their positions in the array must not be the same), remove them from the array, and add ⌊ (a_i)/(a_j) ⌋ to your score, where ⌊ x/y ⌋ is the maximum integer not exceeding x/y.

Initially, your score is 0. After you perform exactly k operations, you add all the remaining elements of the array to the score.

Calculate the minimum possible score you can get.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 500) — the number of test cases.

Each test case consists of two lines. The first line contains two integers n and k (1 ≤ n ≤ 100; 0 ≤ k ≤ ⌊ n/2 ⌋).

The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 2 ⋅ 10^5).

Output

Print one integer — the minimum possible score you can get.

Example

Input


5
7 3
1 1 1 2 1 3 1
5 1
5 5 5 5 5
4 2
1 3 3 7
2 0
4 2
9 2
1 10 10 1 10 2 7 10 3


Output


2
16
0
6
16

Note

Let's consider the example test.

In the first test case, one way to obtain a score of 2 is the following one:

  1. choose a_7 = 1 and a_4 = 2 for the operation; the score becomes 0 + ⌊ 1/2 ⌋ = 0, the array becomes [1, 1, 1, 1, 3]; 
  2. choose a_1 = 1 and a_5 = 3 for the operation; the score becomes 0 + ⌊ 1/3 ⌋ = 0, the array becomes [1, 1, 1]; 
  3. choose a_1 = 1 and a_2 = 1 for the operation; the score becomes 0 + ⌊ 1/1 ⌋ = 1, the array becomes [1]; 
  4. add the remaining element 1 to the score, so the resulting score is 2. 



In the second test case, no matter which operations you choose, the resulting score is 16.

In the third test case, one way to obtain a score of 0 is the following one:

  1. choose a_1 = 1 and a_2 = 3 for the operation; the score becomes 0 + ⌊ 1/3 ⌋ = 0, the array becomes [3, 7]; 
  2. choose a_1 = 3 and a_2 = 7 for the operation; the score becomes 0 + ⌊ 3/7 ⌋ = 0, the array becomes empty; 
  3. the array is empty, so the score doesn't change anymore. 



In the fourth test case, no operations can be performed, so the score is the sum of the elements of the array: 4 + 2 = 6.
1
6 3
4 4 5 5 6 6
 1
6 3
1 1 1 1 2 2
 1
9 3
1 1 1 2 2 2 3 3 3
 1
10 5
3 3 3 4 4 4 5 5 5 1
 1
10 4
1 1 1 2 3 3 3 3 4 5
 1
77 9
9 8 10 5 8 20 17 19 14 16 7 6 15 16 6 13 10 13 14 12 5 6 12 14 12 8 13 12 17 8 12 17 2 11 8 18 17 2 13 2 1 19 9 8 10 20 8 12 15 1 3 15 6 19 4 11 12 8 3 2 1 20 15 14 6 10 11 1 5 11 10 6 20 6 14 16 6
 1
14 7
1 1 1 1 1 1 1 2 2 2 2 2 3 3
 1
88 38
9 143 135 72 74 12 120 27 108 183 18 24 163 122 140 155 166 188 197 14 134 66 188 161 79 100 40 55 161 118 121 18 72 141 136 31 39 187 2 98 16 118 120 196 127 66 135 186 49 16 17 50 107 192 50 23 62 110 83 124 197 127 185 129 131 182 45 147 174 115 89 109 177 7 70 43 75 5 157 93 59 26 176 105 32 89 65 6
 5
7 3
1 1 1 2 1 3 1
5 1
5 5 5 5 5
4 2
1 3 3 7
2 0
4 2
10 5
3 3 3 4 4 4 5 5 5 1
 1
87 12
10 5 11 7 16 16 8 11 14 11 4 4 3 7 16 12 2 3 3 13 1 7 11 16 4 7 11 5 3 15 20 5 12 1 8 8 13 19 3 7 14 3 4 10 18 13 20 1 4 8 10 12 4 7 15 2 18 13 6 2 1 2 10 13 4 5 18 7 1 10 6 2 19 17 5 11 10 12 14 6 16 20 11 12 10 3 6
 1
16 8
1 1 2 2 3 3 3 3 3 3 3 3 3 4 5 5
 1
8 4
1 1 3 3 3 3 5 6
 1
12 6
1 1 1 8 8 8 8 8 8 10 10 10
 5
7 3
1 1 1 2 1 3 1
5 1
5 5 5 5 5
4 2
1 3 3 7
6 3
2 2 3 3 4 4
9 2
1 10 10 1 10 2 7 10 3
 1
12 6
1 1 1 1 1 2 2 2 2 3 3 3
 1
100 34
2 6 5 4 4 4 5 7 6 6 1 2 5 1 4 4 4 5 5 5 2 3 5 6 6 1 1 3 7 5 4 4 1 3 4 6 4 2 7 6 5 4 6 1 1 2 4 6 4 2 2 6 6 3 5 3 4 5 3 4 3 2 1 7 7 5 4 6 3 1 6 7 6 2 2 2 4 7 3 2 6 1 1 3 1 5 6 4 4 7 2 6 6 5 4 4 3 5 2 4
 1
85 3
43 17 34 67 14 7 80 48 36 95 48 68 86 4 17 46 51 87 41 90 100 56 57 42 9 8 27 23 16 14 99 22 13 98 89 24 77 59 15 94 25 81 4 71 24 43 97 88 97 10 6 8 3 86 28 61 100 98 76 85 32 18 79 66 51 44 28 99 87 56 80 93 89 76 7 57 96 39 46 25 4 67 6 51 39
 1
6 3
1 1 2 2 3 3
 1
6 3
2 3 3 3 4 4
 1
6 3
1 7 7 7 10 10
 1
10 3
1 7 4 3 2 2 6 7 4 7
 1
100 17
5 1 1 7 3 2 5 1 1 3 4 5 5 5 7 5 7 5 1 7 6 6 1 3 6 3 4 5 4 6 3 1 7 6 2 3 2 5 3 3 6 5 5 6 5 7 5 3 5 4 7 3 5 1 7 3 4 4 3 3 3 5 1 1 1 7 1 3 2 3 2 7 2 1 6 5 6 6 1 5 4 6 1 7 6 7 6 1 1 1 5 3 5 7 4 6 4 6 3 2
 1
7 3
1 1 1 2 2 3 3
 1
9 2
1 10 10 1 10 2 7 10 191919
 1
6 3
6 6 5 5 1 1
 1
8 3
1 1 6 6 6 6 2 2
 1
91 9
4 3 19 8 3 6 16 5 17 11 9 13 15 8 1 3 20 2 19 7 14 1 6 4 8 18 13 8 16 11 3 12 3 3 12 17 15 9 5 15 12 11 7 20 19 3 4 14 10 9 7 16 12 10 3 6 15 17 4 8 15 2 10 13 11 15 7 20 1 10 9 2 10 15 7 1 6 16 2 1 17 10 19 10 7 18 3 5 10 12 15
 1
67 22
83 41 94 76 47 33 20 51 98 48 92 72 24 51 15 17 35 70 83 95 79 65 80 17 72 7 97 14 74 98 55 63 45 79 42 92 85 24 84 30 29 77 64 68 68 71 89 18 82 68 20 91 84 52 45 23 65 95 83 84 18 81 63 11 89 41 69
 1
4 2
5 6 5 5
 1
6 3
3 3 4 4 7 7
 10
7 3
2 2 2 2 3 3 3
7 3
2 2 3 3 3 4 4
7 3
2 2 2 2 2 2 2
7 3
2 2 3 3 3 4 4
7 3
2 2 2 3 3 3 3
7 3
2 2 3 3 3 3 4
7 3
2 2 2 2 2 3 3
7 3
2 2 3 3 3 3 3
7 3
2 2 2 2 2 2 3
7 3
2 2 2 3 3 3 4
 1
7 3
2 2 2 2 7 8 2
 1
13 6
1 2 2 2 2 3 3 3 3 4 4 4 4
 1
10 3
1 1 1 1 1 1 2 2 3 3
 1
10 3
2 15 14 13 12 15 18 2 9 15
 1
8 4
1 2 2 2 2 3 3 3

0
 1
 3
 0
 2
 489
 0
 140
 2
16
0
6
0
 401
 1
 0
 0
 2
16
0
0
16
 0
 58
 3753
 0
 0
 0
 8
 192
 1
 22
 0
 3
 569
 616
 1
 0
 2
2
5
2
3
3
3
4
4
2
 3
 1
 4
 25
 0

import java.io.*;
import java.util.*;
import java.util.concurrent.ThreadLocalRandom;
import java.math.*;

/**
 __                  __
 ( _)                ( _)
 / / \\              / /\_\_
 / /   \\            / / | \ \
 / /     \\          / /  |\ \ \
 /  /   ,  \ ,       / /   /|  \ \
 /  /    |\_ /|      / /   / \   \_\
 /  /  |\/ _ '_| \   / /   /   \    \\
 |  /   |/  0 \0\    / |    |    \    \\
 |    |\|      \_\_ /  /    |     \    \\
 |  | |/    \.\ o\o)  /      \     |    \\
 \    |     /\\`v-v  /        |    |     \\
 | \/    /_| \\_|  /         |    | \    \\
 | |    /__/_ `-` /   _____  |    |  \    \\
 \|    [__]  \_/  |_________  \   |   \    ()
 /    [___] (    \         \  |\ |   |   //
 |    [___]                  |\| \|   /  |/
 /|    [____]                  \  |/\ / / ||
 (  \   [____ /     ) _\      \  \    \| | ||
 \  \  [_____|    / /     __/    \   / / //
 |   \ [_____/   / /        \    |   \/ //
 |   /  '----|   /=\____   _/    |   / //
 __ /  /        |  /   ___/  _/\    \  | ||
 (/-(/-\)       /   \  (/\/\)/  |    /  | /
 (/\/\)           /   /   //
 _________/   /    /
 \____________/    (


 @author NTUDragons-Reborn
 */

public class C{
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task solver = new Task();
        solver.solve(in, out);
        out.close();
    }
    // main solver
    static class Task{

        double eps= 0.00000001;
        static final int MAXN = 200015;
        static final int MOD= 998244353;

        // stores smallest prime factor for every number
        static int spf[] = new int[MAXN];

        static boolean[] prime;

        Map<Integer,Set<Integer>> dp= new HashMap<>();

        // Calculating SPF (Smallest Prime Factor) for every
        // number till MAXN.
        // Time Complexity : O(nloglogn)
        public void sieve()
        {
            spf[1] = 1;
            for (int i=2; i<MAXN; i++)

                // marking smallest prime factor for every
                // number to be itself.
                spf[i] = i;

            // separately marking spf for every even
            // number as 2
            for (int i=4; i<MAXN; i+=2)
                spf[i] = 2;

            for (int i=3; i*i<MAXN; i++)
            {
                // checking if i is prime
                if (spf[i] == i)
                {
                    // marking SPF for all numbers divisible by i
                    for (int j=i*i; j<MAXN; j+=i)

                        // marking spf[j] if it is not
                        // previously marked
                        if (spf[j]==j)
                            spf[j] = i;
                }
            }
        }

        void sieveOfEratosthenes(int n)
        {
            // Create a boolean array
            // "prime[0..n]" and
            // initialize all entries
            // it as true. A value in
            // prime[i] will finally be
            // false if i is Not a
            // prime, else true.
            prime= new boolean[n + 1];
            for (int i = 0; i <= n; i++)
                prime[i] = true;
    
            for (int p = 2; p * p <= n; p++)
            {
                // If prime[p] is not changed, then it is a
                // prime
                if (prime[p] == true)
                {
                    // Update all multiples of p
                    for (int i = p * p; i <= n; i += p)
                        prime[i] = false;
                }
            }
        }

        // A O(log n) function returning primefactorization
        // by dividing by smallest prime factor at every step
        public Set<Integer> getFactorization(int x)
        {
            if(dp.containsKey(x)) return dp.get(x);
            Set<Integer> ret = new HashSet<>();
            while (x != 1)
            {
                if(spf[x]!=2) ret.add(spf[x]);
                x = x / spf[x];
            }
            dp.put(x,ret);
            return ret;
        }
        // function to find first index >= x
        public int lowerIndex(List<Integer> arr, int n, int x)
        {
            int l = 0, h = n - 1;
            while (l <= h)
            {
                int mid = (l + h) / 2;
                if (arr.get(mid) >= x)
                    h = mid - 1;
                else
                    l = mid + 1;
            }
            return l;
        }
        public int lowerIndex(int[] arr, int n, int x)
        {
            int l = 0, h = n - 1;
            while (l <= h)
            {
                int mid = (l + h) / 2;
                if (arr[mid] >= x)
                    h = mid - 1;
                else
                    l = mid + 1;
            }
            return l;
        }

        // function to find last index <= y
        public int upperIndex(List<Integer> arr, int n, int y)
        {
            int l = 0, h = n - 1;
            while (l <= h)
            {
                int mid = (l + h) / 2;
                if (arr.get(mid) <= y)
                    l = mid + 1;
                else
                    h = mid - 1;
            }
            return h;
        }
        public int upperIndex(int[] arr, int n, int y)
        {
            int l = 0, h = n - 1;
            while (l <= h)
            {
                int mid = (l + h) / 2;
                if (arr[mid] <= y)
                    l = mid + 1;
                else
                    h = mid - 1;
            }
            return h;
        }

        // function to count elements within given range
        public int countInRange(List<Integer> arr, int n, int x, int y)
        {
            // initialize result
            int count = 0;
            count = upperIndex(arr, n, y) -
                    lowerIndex(arr, n, x) + 1;
            return count;
        }

        public int add(int a, int b){
            a+=b;
            while(a>=MOD) a-=MOD;
            while(a<0) a+=MOD;
            return a;
        }

        public int mul(int a, int b){
            long res= (long)a*(long)b;
            return (int)(res%MOD);
        }

        public int power(int a, int b) {
            int ans=1;
            while(b>0){
                if((b&1)!=0) ans= mul(ans,a);
                b>>=1;
                a= mul(a,a);
            }
            return ans;
        }

        int[] fact= new int[MAXN];
        int[] inv= new int[MAXN];

        public int Ckn(int n, int k){
            if(k<0 || n<0) return 0;
            if(n<k) return 0;
            return mul(mul(fact[n],inv[k]),inv[n-k]);
        }

        public int inverse(int a){
            return power(a,MOD-2);
        }

        public void preprocess() {
            fact[0]=1;
            for(int i=1;i<MAXN;i++) fact[i]= mul(fact[i-1],i);
            inv[MAXN-1]= inverse(fact[MAXN-1]);
            for(int i=MAXN-2;i>=0;i--){
                inv[i]= mul(inv[i+1],i+1);
            }
        }

        /**
         * return VALUE of lower bound for unsorted array
         */
        public int lowerBoundNormalArray(int[] arr, int x){
            TreeSet<Integer> set= new TreeSet<>();
            for(int num: arr) set.add(num);
            return set.lower(x);
        }
        /**
         * return VALUE of upper bound for unsorted array
         */
        public int upperBoundNormalArray(int[] arr, int x){
            TreeSet<Integer> set= new TreeSet<>();
            for(int num: arr) set.add(num);
            return set.higher(x);
        }

        public void debugArr(int[] arr){
            for(int i: arr) out.print(i+" ");
            out.println();
        }

        public int rand(){
            int min=0, max= MAXN;
            int random_int = (int)Math.floor(Math.random()*(max-min+1)+min);
            return random_int;
        }
        
        public void suffleSort(int[] arr){
            shuffleArray(arr);
            Arrays.sort(arr);
        }


        public void shuffleArray(int[] ar)
        {
            // If running on Java 6 or older, use `new Random()` on RHS here
            Random rnd = ThreadLocalRandom.current();
            for (int i = ar.length - 1; i > 0; i--)
            {
            int index = rnd.nextInt(i + 1);
            // Simple swap
            int a = ar[index];
            ar[index] = ar[i];
            ar[i] = a;
            }
        }
        
        InputReader in; PrintWriter out;
        CustomFileReader cin;
        int[] xor= new int[3*100000+5];
        int[] pow2= new int[1000000+1];
        public void solve(InputReader in, PrintWriter out) {
            this.in=in; this.out=out;
            // sieve();
            // pow2[0]=1;
            // for(int i=1;i<pow2.length;i++){
            //     pow2[i]= mul(pow2[i-1],2);
            // }
            int t= in.nextInt();
            preprocess();
            // int t=in.nextInt();
            // int t= cin.nextIntArrLine()[0];
            for(int i=1;i<=t;i++) solveD(i);
        }
    
        final double pi= Math.acos(-1);
        static Point base;

        void solveA(int t) {
            int[] b= new int[7];
            for(int i=0;i<7;i++) b[i]= in.nextInt();
            Arrays.sort(b);
            if (b[0] + b[1] != b[2]) out.println( b[0] + " " + b[1] + " " + b[2]);
            else out.println(b[0] + " " + b[1] + " " + b[3]);
        }
        
        void solveB(int t) {
            int n= in.nextInt();
            List<Character> ans= new ArrayList<>();
            for (int i=0; i<n-2; i++) {
                char[] x= in.nextToken().toCharArray();
                if (ans.size()==0 ) { 
                    ans.add(x[0]); 
                    ans.add(x[1]);
                }
                else if (x[0] == ans.get(ans.size()-1)) ans.add(x[1]);
                else {
                    ans.add(x[0]);
                    ans.add(x[1]);
                }
            }
            if (ans.size() != n) ans.add('a');
            for (int i=0; i<n; i++) out.print(ans.get(i));
            out.println();
        }
        
        // int gcd(int a, int b) {
        //     if (b == 0)
        //         return a;
        //     return gcd(b, a % b);
             
        // }
        
        long help(long[] a, long n, int start) {
            long res = a[start];
            if (start == 1) {
                res = a[1];
                for (int i=1; i<=n; i+=2) res = _gcd(res, a[i]);
                if (res == 1) return 0;
                for (int i=2; i<=n; i+=2) if (a[i] % res == 0) return 0;
            }
            else {
                res = a[2];
                for (int i=2; i<=n; i+=2) res = _gcd(res, a[i]);
                if (res == 1) return 0;
                for (int i=1; i<=n; i+=2) if (a[i] % res == 0) return 0;
            }
            return res;
        }
        void solveC(int t) {
            long n= in.nextLong();
            long[] a= new long[(int)n+2];
            for (int i=1; i<=n; i++) a[i]= in.nextLong();
            
            long ans = help(a, n, 1);
            if (ans == 0) ans = help(a, n, 2);
            out.println(ans);
        }
        
        void solveD(int t) {
            int n= in.nextInt(), k= in.nextInt();
            long[] a= new long[n];
            Map<Long, Long> count= new HashMap<>();
            for (int i=0; i<n; i++) a[i]= in.nextLong();
            Arrays.sort(a);
        
            long ans = 0;
            for (int i=0; i<n-2*k; i++) ans += a[i];
        
            long add = 0;
            for (int i=n-2*k; i<n; i++) {
                count.put(a[i], count.getOrDefault(a[i], 0l)+1);
                add = Math.max(add, count.getOrDefault(a[i], 0l));
            }
        
            if (add - k < 0) out.println(ans);
            else out.println(ans + (add - k));
        }
        

        private int mode(int n, int base){
            if(n>=  base) return n%base;
            else{
                int k= Math.abs(n)/base;
                return (n+(k+1)*base)%base;
            }
        }
        



        static class Node implements Comparable<Node>{
            char op;
            int s;
            public Node (char op, int s) {
                this.op= op;
                this.s= s;
            }
            @Override
            public int compareTo(Node o) {
                if (this.s==o.s) return (int)(this.op-o.op);
                return this.s-o.s;
            }

        }

        private long distance(Point p1, Point p2) {
            long x= p1.x-p2.x, y= p1.y-p2.y;
            return x*x+y*y;
        }


        private boolean eqPoint(Point p1, Point p2){
            return p1.x==p2.x && p1.y==p2.y;
        }

        private double polarAngle(Point p1, Point p2) {
            // p1 -> p2
            if (p1.x==p2.x) return pi/2;
            else if (p1.y==p2.y){
                if(p1.x<p2.x) return 0;
                else return pi;
            }
            else {
                double y= (double)p2.y-(double)p1.y;
                double x= (double)p2.x-(double)p1.x;
                BigDecimal alpha1= new BigDecimal(y);
                BigDecimal alpha2= new BigDecimal(x);
                BigDecimal val= alpha1.divide(alpha2);

                double angle= Math.atan(val.doubleValue());
                if (angle<0) angle+= pi;
                out.println("angle: "+angle);
                return angle;
            }
        }

        private boolean isRightTurn(Point p1, Point p2, Point p3){
            Vector v1= new Vector(p1,p2), v2= new Vector(p1,p3);
            if(crossProd(v1,v2)<0) return true;
            else return false;
        }

        private long crossProd(Vector v1, Vector v2){
            //x1*y2-x2*y1
            return v1.x*v2.y - v2.x*v1.y;
        }

        static class PointAngle implements Comparable<PointAngle>{
            Point p;
            double angle;
            long dis;
            public PointAngle(Point p, double angle, long dis) {
                this.p= p;
                this.angle= angle;
                this.dis= dis;

            }

            @Override
            public int compareTo(PointAngle o) {
                double dif= this.angle-o.angle;
                if (dif <0) return -1;
                else if(dif >0) return 1;
                else {
                    long dif2r= this.dis-o.dis;
                    long dif2l= o.dis-this.dis;

                    if (base.x < this.p.x) return intDif(dif2r);
                    else return intDif(dif2l); 
                    
                }
            }

            private int intDif(long a){
                if (a>0) return 1;
                else if(a<0) return -1;
                else return 0;
            }
        }


    
        
        public long _gcd(long a,  long b)
        {

            if(b == 0) {
                return a;
            }
            else {
                return _gcd(b, a % b);
            }
        }
        public long _lcm(long a, long b){
            return (a*b)/_gcd(a,b);
        }

    }


    // static class SEG {

    //     Pair[] segtree;
        
    //     public SEG(int n){
            
    //         segtree= new Pair[4*n];
    //         Arrays.fill(segtree, new Pair(-1,Long.MAX_VALUE));
    //     }
    //     // void buildTree(int l, int r, int index) {
    //     //     if (l == r) {
    //     //         segtree[index].y = a[l];
    //     //         return;
    //     //     }
    //     //     int mid = (l + r) / 2;
    //     //     buildTree(l, mid, 2 * index + 1);
    //     //     buildTree(mid + 1, r, 2 * index + 2);
    //     //     segtree[index].y = Math.min(segtree[2 * index + 1].y, segtree[2 * index + 2].y);
    //     // }
        
    //     void update(int l, int r, int index, int pos, Pair val) {
    //         if (l == r) {
    //             segtree[index] = val;
    //             return;
    //         }
    //         int mid = (l + r) / 2;
    //         if (pos <= mid) update(l, mid, 2 * index + 1, pos, val);
    //         else update(mid + 1, r, 2 * index + 2, pos, val);
    //         if(segtree[2 * index + 1].y < segtree[2 * index + 2].y){
    //             segtree[index]= segtree[2 * index + 1];
    //         }
    //         else {
    //             segtree[index]= segtree[2 * index + 2];
    //         }
    //     }
        
    //     // Pair query(int l, int r, int from, int to, int index) {
    //     //     if (from <= l && r <= to)
    //     //         return segtree[index];
    //     //     if (r < from | to < l)
    //     //         return 0;
    //     //     int mid = (l + r) / 2;
    //     //     Pair left= query(l, mid, from, to, 2 * index + 1);
    //     //     Pair right= query(mid + 1, r, from, to, 2 * index + 2);
    //     //     if(left.y < right.y) return left;
    //     //     else return right;
            
    //     // }
        
        
    // }

    static class Venice{
        public Map<Long,Long> m= new HashMap<>();
        public long base=0;
        public long totalValue=0;
        private int M= 1000000007;

        private long addMod(long a, long b){
            a+=b;
            if(a>=M) a-=M;
            return a;
        }

        public void reset(){
            m= new HashMap<>();
            base=0;
            totalValue=0;
        }
        public void update(long add){
            base= base+ add;
        }
        public void add(long key, long val){
            long newKey= key-base;
            m.put(newKey, addMod(m.getOrDefault(newKey,(long)0),val));
        }
    }



    static class Tuple implements Comparable<Tuple>{
        int x, y, z;
        public Tuple(int x, int y, int z){
            this.x= x;
            this.y= y;
            this.z=z;
        }
        @Override
        public int compareTo(Tuple o){
            return this.z-o.z;
        }
    }

    static class Point implements Comparable<Point>{
        public long x;
        public long y;
        public Point(long x, long y){
            this.x= x;
            this.y= y;
        }

        @Override
        public int compareTo(Point o) {
            if(this.y!=o.y) return (int)(this.y-o.y);
            return (int)(this.x-o.x);
        }
    }

    static class Vector {
        public long x;
        public long y;

        // p1 -> p2
        public Vector(Point p1, Point p2){
            this.x= p2.x-p1.x;
            this.y= p2.y-p1.y;
        }
    }

    static class Pair implements Comparable<Pair>{
        public int x;
        public int y;
        public Pair(int x, int y){
            this.x= x;
            this.y= y;
        }

        @Override
        public int compareTo(Pair o) {
            if(this.x!=o.x) return this.x-o.x;
            return (int)(this.y-o.y);
        }
    }

    // public static class compareL implements Comparator<Tuple>{
    //     @Override
    //     public int compare(Tuple t1, Tuple t2) {
    //         return t2.l - t1.l;
    //     }
    // }

    // fast input reader class;
    static class InputReader {
        BufferedReader br;
        StringTokenizer st;

        public InputReader(InputStream stream) {
            br = new BufferedReader(new InputStreamReader(stream));
        }

        public String nextToken() {
            while (st == null || !st.hasMoreTokens()) {
                String line = null;
                try {
                    line = br.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
                if (line == null) {
                    return null;
                }
                st = new StringTokenizer(line);
            }
            return st.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(nextToken());
        }
        public double nextDouble(){
            return Double.parseDouble(nextToken());
        }
        public long nextLong(){
            return Long.parseLong(nextToken());
        }
        public int[] nextIntArr(int n){
            int[] arr= new int[n];
            for(int i=0;i<n;i++) arr[i]= nextInt();
            return arr;
        }
        public long[] nextLongArr(int n){
            long[] arr= new long[n];
            for(int i=0;i<n;i++) arr[i]= nextLong();
            return arr;
        }
        public List<Integer> nextIntList(int n){
            List<Integer> arr= new ArrayList<>();
            for(int i=0;i<n;i++) arr.add(nextInt());
            return arr;
        }
        public int[][] nextIntMatArr(int n, int m){
            int[][] mat= new int[n][m];
            for(int i=0;i<n;i++) for(int j=0;j<m;j++) mat[i][j]= nextInt();
            return mat;
        }
        public List<List<Integer>> nextIntMatList(int n, int m){
            List<List<Integer>> mat= new ArrayList<>();
            for(int i=0;i<n;i++){
                List<Integer> temp= new ArrayList<>();
                for(int j=0;j<m;j++) temp.add(nextInt());
                mat.add(temp);
            }
            return mat;
        }
        public char[] nextStringCharArr(){
            return nextToken().toCharArray();
        }
    }

    static class CustomFileReader{
        String path="";
        Scanner sc;
        public CustomFileReader(String path){
            this.path=path;
            try{
                sc= new Scanner(new File(path));
            }
            catch(Exception e){}
        }
        public String nextLine(){
            return sc.nextLine();
        }
        public int[] nextIntArrLine(){
            String line= sc.nextLine();
            String[] part= line.split("[\\s+]");
            int[] res= new int[part.length];
            for(int i=0;i<res.length;i++) res[i]= Integer.parseInt(part[i]);
            return res;
        }
    }
}