Polycarp often uses his smartphone. He has already installed n applications on it. Application with number i takes up a_i units of memory.

Polycarp wants to free at least m units of memory (by removing some applications).

Of course, some applications are more important to Polycarp than others. He came up with the following scoring system — he assigned an integer b_i to each application: 

  * b_i = 1 — regular application; 
  * b_i = 2 — important application. 



According to this rating system, his phone has b_1 + b_2 + … + b_n convenience points.

Polycarp believes that if he removes applications with numbers i_1, i_2, …, i_k, then he will free a_{i_1} + a_{i_2} + … + a_{i_k} units of memory and lose b_{i_1} + b_{i_2} + … + b_{i_k} convenience points.

For example, if n=5, m=7, a=[5, 3, 2, 1, 4], b=[2, 1, 1, 2, 1], then Polycarp can uninstall the following application sets (not all options are listed below): 

  * applications with numbers 1, 4 and 5. In this case, it will free a_1+a_4+a_5=10 units of memory and lose b_1+b_4+b_5=5 convenience points; 
  * applications with numbers 1 and 3. In this case, it will free a_1+a_3=7 units of memory and lose b_1+b_3=3 convenience points. 
  * applications with numbers 2 and 5. In this case, it will free a_2+a_5=7 memory units and lose b_2+b_5=2 convenience points. 



Help Polycarp, choose a set of applications, such that if removing them will free at least m units of memory and lose the minimum number of convenience points, or indicate that such a set does not exist.

Input

The first line contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases. Then t test cases follow.

The first line of each test case contains two integers n and m (1 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ m ≤ 10^9) — the number of applications on Polycarp's phone and the number of memory units to be freed.

The second line of each test case contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9) — the number of memory units used by applications.

The third line of each test case contains n integers b_1, b_2, …, b_n (1 ≤ b_i ≤ 2) — the convenience points of each application.

It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5.

Output

For each test case, output on a separate line: 

  * -1, if there is no set of applications, removing which will free at least m units of memory; 
  * the minimum number of convenience points that Polycarp will lose if such a set exists. 

Example

Input


5
5 7
5 3 2 1 4
2 1 1 2 1
1 3
2
1
5 10
2 3 2 3 2
1 2 1 2 1
4 10
5 1 3 4
1 2 1 2
4 5
3 2 1 2
2 1 2 1


Output


2
-1
6
4
3

Note

In the first test case, it is optimal to remove applications with numbers 2 and 5, freeing 7 units of memory. b_2+b_5=2.

In the second test case, by removing the only application, Polycarp will be able to clear only 2 of memory units out of the 3 needed.

In the third test case, it is optimal to remove applications with numbers 1, 2, 3 and 4, freeing 10 units of memory. b_1+b_2+b_3+b_4=6.

In the fourth test case, it is optimal to remove applications with numbers 1, 3 and 4, freeing 12 units of memory. b_1+b_3+b_4=4.

In the fifth test case, it is optimal to remove applications with numbers 1 and 2, freeing 5 units of memory. b_1+b_2=3.
// package eround101;

import java.util.*;
import java.io.*;
import java.lang.*;
import java.util.StringTokenizer;

public class C101 {

    static HritikScanner sc = new HritikScanner();
    static  PrintWriter pw = new PrintWriter(System.out,true);
    final static int MOD = (int) (1e9 + 7);
    static int[] count = new int[1000001];
    static StringBuilder sb = new StringBuilder();

    
        public static void main(String[] args) {

        int t = sc.nextInt();
        while (t-- > 0)
            solve();
        }

     static void solve(){
//        int n = ni();    
//        long[] arr = new long[n];
//        for(int i = 0; i < n; i++)
//        {
//            arr[i] = nl();
//        }
        int n = ni();
        int m = ni();
        int[][] arr = new int[n][2];
        for(int i = 0; i < n; i++)
        {
            arr[i][0] = ni();
        }
        for(int i = 0; i < n; i++)
        {
            arr[i][1] = ni();
        }
        ArrayList<Integer> one = new ArrayList<>();
        ArrayList<Integer> two = new ArrayList<>();
        long sumA = 0, sumB = 0;
        for(int i = 0; i < n; i++)
        {
            if(arr[i][1] == 1)
            {
                one.add(arr[i][0]);
            }
            else
            {
                two.add(arr[i][0]);
                sumB += arr[i][0];
            }
        }
        Collections.sort(one, Collections.reverseOrder());
        Collections.sort(two, Collections.reverseOrder());
        int b = two.size();
        int ans = Integer.MAX_VALUE;
        for(int j = 0; j <= one.size(); j++)
        {
            while(b > 0 && sumA + sumB - two.get(b-1) >= m)
            {
                b--;
                sumB -= two.get(b);
            }
            if(sumA + sumB >= m)
            {
                ans = Math.min(ans, 2*b + j);
            }
            if(j != one.size())
            {
                sumA += one.get(j);
            }
        }
        if(ans == Integer.MAX_VALUE)
        {
            pl(-1);
        }
        else
            pl(ans);
    }
     
     
    /////////////////////////////////////////////////////////////////////////////////
    
    static int ni() 
    {
        return sc.nextInt();
    }
    static long nl() 
    {
        return sc.nextLong();
    }
    static double nd() 
    {
        return sc.nextDouble();
    }
    
    /////////////////////////////////////////////////////////////////////////////////
    
    static void pl()
    {
        pw.println();
    }
    static void p(Object o)
    {
        pw.print(o);
    }
    static void pl(Object o)
    {
        pw.println(o);
    }
    static void psb(StringBuilder sb)
    {
        pw.print(sb);
    }
    static void pa(Object arr[])
    {
        for(Object o : arr)
            p(o);
        pl();
    }
    static void pa(int arr[])
    {
        for(int o : arr)
            p(o);
        pl();
    }
    static void pa(long arr[])
    {
        for(long o : arr)
            p(o);
        pl();
    }
    static void pa(double arr[])
    {
        for(double o : arr)
            p(o);
        pl();
    }
    static void pa( char arr[])
    {
        for(char o : arr)
            p(o);
        pl();
    }
    static void pa(List list)
    {
        for(Object o : list)
            p(o);
        pl();
    }
    static void pa(Object[][] arr) {
     
        for(int i=0;i<arr.length;++i) {
            for(Object o : arr[i])
                p(o);
            pl();
        }
    }
    static void pa(int[][] arr) {
        for(int i=0;i<arr.length;++i) {
            for(int o : arr[i])
                p(o);
            pl();
        }
    }
    static void pa(long[][] arr) {
        for(int i=0;i<arr.length;++i) {
            for(long o : arr[i])
                p(o);
            pl();
        }
    }
    static void pa(char[][] arr) {
        for(int i=0;i<arr.length;++i) {
            for(char o : arr[i])
                p(o);
            pl();
        }
    }
    static void pa(double[][] arr) {
        for(int i=0;i<arr.length;++i) {
            for(double o : arr[i])
                p(o);
            pl();
        }
    }

/////////////////////////////////////////////////////////////////////////////////


    

    static void print(Object s) {
        System.out.println(s);
    }
    
    
    
    /////////////////////////////////////////////////////////////////////////////////

    
    //-----------HritikScanner class for faster input----------//
    static class HritikScanner {

        BufferedReader br;
        StringTokenizer st;

        public HritikScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
    
    

    //////////////////////////////////////////////////////////////////
    public static class Pair implements Comparable<Pair> {

        int h, w, index;

        Pair(int h, int w) {
            this.h = h;
            this.w = w;
            
        }

        public int compareTo(Pair A) {
            if (A.h == this.h) {
                return this.w - A.w;
            }
            return this.h - A.h;
        }
    }
    
     //////////////////////////////////////////////////////////////////
    
    // Function to return gcd of a and b time complexity O(log(a+b))
    static int gcd(int a, int b) 
    { 
        if (a == 0) 
            return b; 
        return gcd(b % a, a); 
    } 
    
      //////////////////////////////////////////////////////////////////

    static boolean isPrime(long n) 
    { 
        // Corner cases 
        if (n <= 1) return false; 
        if (n <= 3) return true; 
      
        // This is checked so that we can skip  
        // middle five numbers in below loop 
        if (n % 2 == 0 || n % 3 == 0) return false; 
      
        for (long i = 5; i * i <= n; i = i + 6) 
            if (n % i == 0 || n % (i + 2) == 0) 
            return false; 
      
        return true; 
    } 
    static boolean isPowerOfTwo(long n)
    {
        if(n==0)
        return false;
 
        return (long)(Math.ceil((Math.log(n) / Math.log(2)))) == 
         (long)(Math.floor(((Math.log(n) / Math.log(2)))));
    }
//    static int nCr(int n, int r) 
//{ 
//    return fact(n) / (fact(r) * 
//                  fact(n - r)); 
//} 
//  
//// Returns factorial of n 
//static int fact(int n) 
//{ 
//    int res = 1; 
//    for (int i = 2; i <= n; i++) 
//        res = res * i; 
//    return res; 
//} 
    public static long getFact(int n){
        long ans = 1;
        while (n > 0){
            ans *= n;
            ans %= MOD;
            n--;
        }
        return ans;
    }
    public static long pow(long n, int pow){
        if (pow == 0)
            return 1;
        long temp = pow(n, pow/2)%MOD;
        temp *= temp;
        temp %= MOD;
        if (pow % 2 == 1)
            temp *= n;
        temp %= MOD;
        return temp;
 
    }
    public static long nCr(int n, int r){
        long ans = 1;
        int temp = n-r;
        while (n > temp){
            ans *= n;
            ans %= MOD;
            n--;
        }
        ans *= pow(getFact(r)%MOD, MOD-2)%MOD;
        ans %= MOD;
        return ans;
    }
    

}
