You are given n integers a_1, a_2, …, a_n and an integer k. Find the maximum value of i ⋅ j - k ⋅ (a_i | a_j) over all pairs (i, j) of integers with 1 ≤ i < j ≤ n. Here, | is the [bitwise OR operator](https://en.wikipedia.org/wiki/Bitwise_operation#OR).

Input

The first line contains a single integer t (1 ≤ t ≤ 10 000) — the number of test cases.

The first line of each test case contains two integers n (2 ≤ n ≤ 10^5) and k (1 ≤ k ≤ min(n, 100)).

The second line of each test case contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ n).

It is guaranteed that the sum of n over all test cases doesn't exceed 3 ⋅ 10^5.

Output

For each test case, print a single integer — the maximum possible value of i ⋅ j - k ⋅ (a_i | a_j).

Example

Input


4
3 3
1 1 3
2 2
1 2
4 3
0 1 2 3
6 6
3 2 0 0 5 6


Output


-1
-4
3
12

Note

Let f(i, j) = i ⋅ j - k ⋅ (a_i | a_j).

In the first test case, 

  * f(1, 2) = 1 ⋅ 2 - k ⋅ (a_1 | a_2) = 2 - 3 ⋅ (1 | 1) = -1. 
  * f(1, 3) = 1 ⋅ 3 - k ⋅ (a_1 | a_3) = 3 - 3 ⋅ (1 | 3) = -6. 
  * f(2, 3) = 2 ⋅ 3 - k ⋅ (a_2 | a_3) = 6 - 3 ⋅ (1 | 3) = -3. 



So the maximum is f(1, 2) = -1.

In the fourth test case, the maximum is f(3, 4) = 12.
// HOPE

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import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.math.BigInteger;
import java.util.*;

public class Codeforces1 {
    static final int mod=1_000_000_007;

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            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 void main(String[] args) {
        FastReader s = new FastReader();
        int t = s.nextInt();
        while(t-->0)
        {
            int n = s.nextInt();
            int k = s.nextInt();
            int[] a = new int[n+1];

            Pair[] p = new Pair[n];
            Pair[] pp = new Pair[n];

            for(int i=1;i<=n;i++)
            {
                a[i] = s.nextInt();
            }
            for(int i=0;i<n;i++)
            {
                p[i] = new Pair(a[i+1], i+1);
                pp[i] = new Pair(a[i+1], i+1);
            }

            Arrays.sort(p,new MyCmp());
            Arrays.sort(pp,new MyCmp1());

            //System.out.println(Arrays.toString(pp));

            long max = Long.MIN_VALUE;
            for(int i=0;i<n-1;i++)
            {
                long val1 = ((long) p[i].y *p[i+1].y);
               long val2 = (long) k * (p[i].x | p[i+1].x);

                long val3 = ((long) pp[i].y *pp[i+1].y);
                long val4 = (long) k * (pp[i].x | pp[i+1].x);
               long val = val1-val2;
               long vall = val3-val4;

               long res = Math.max(val, vall);
               max = Math.max(max, res);
            }
            System.out.println(max);
        }
    }












    /////////////////////////////////////////////////THE END///////////////////////////////////////////////////////////
    //////////////////////////////////////////////////////////////////////////////////////////////////////////////////

    public static int gcd(int x,int y)
    {
        return y==0?x:gcd(y,x%y);
    }
    public static long gcd(long x,long y)
    {
        return y==0L?x:gcd(y,x%y);
    }

    public static int lcm(int a, int b) {
        return (a * b) / gcd(a, b);
    }
    public static long lcm(long a, long b) {
        return (a * b) / gcd(a, b);
    }

    public static long pow(long a,long b)
    {
        if(b==0L)
            return 1L;
        long tmp=1;
        while(b>1L)
        {
            if((b&1L)==1)
                tmp*=a;
            a*=a;
            b>>=1;
        }
        return (tmp*a);
    }

    public static long modPow(long a,long b,long mod)
    {
        if(b==0L)
            return 1L;
        long tmp=1;
        while(b>1L)
        {
            if((b&1L)==1L)
                tmp*=a;

            a*=a;
            a%=mod;
            tmp%=mod;
            b>>=1;
        }
        return (tmp*a)%mod;
    }

    static long mul(long a, long b) {
        return a*b%mod;
    }

    static long fact(int n) {
        long ans=1;
        for (int i=2; i<=n; i++) ans=mul(ans, i);
        return ans;
    }

    static long fastPow(long base, long exp) {
        if (exp==0) return 1;
        long half=fastPow(base, exp/2);
        if (exp%2==0) return mul(half, half);
        return mul(half, mul(half, base));
    }

    static boolean check(int n,int d)//check for digit 7 in 504732 number
    {
        String s = n+"";
        return s.contains(d + "");
    }
    static void reverseArray(int[] a) {
        int n = a.length;
        int[] arr = new int[n];
        for (int i = 0; i < n; i++)
            arr[i] = a[n - i - 1];
        for (int i = 0; i < n; i++)
            a[i] = arr[i];
    }

    static void reverseArray(long[] a) {
        int n = a.length;
        long[] arr = new long[n];
        for (int i = 0; i < n; i++)
            arr[i] = a[n - i - 1];
        for (int i = 0; i < n; i++)
            a[i] = arr[i];
    }

    static class Pair{
        int x, y;
        Pair(int x, int y)
        {
            this.x = x;
            this.y = y;
        }

        @Override
        public String toString() {
            return "Pair{" +
                    "x=" + x +
                    ", y=" + y +
                    '}';
        }
    }
    static class MyCmp implements Comparator<Pair>
    {
        public int compare(Pair p1, Pair p2)
        {
            return ((p1.x==p2.x)?
                    (p2.y-p1.y):
                    (p1.x-p2.x));
        }
    }
    static class MyCmp1 implements Comparator<Pair>
    {
        public int compare(Pair p1, Pair p2)
        {
            return p2.y-p1.y;//Descending order
        }
    }
}
