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

public class Coder {
  static int n,k;
  static List<long[]> list;
  static StringBuffer str=new StringBuffer();

  static void solve() {
      Collections.sort(list, (a,b)->{
          if(a[0]==b[0]) return (int)(b[1]-a[1]);
          else return (int)(a[0]-b[0]);
      });
      long min=list.get(0)[0];
      long minidx=list.get(0)[1];
      long ans=Long.MIN_VALUE;
      for(int i=1;i<n;i++){
          long min2idx=list.get(i)[1];
          long min2=list.get(i)[0];
          ans=Math.max(ans, (minidx*min2idx)-(k*(min|min2)));
      }
      long ans2=Long.MIN_VALUE;
      min=list.get(n-1)[0];
      minidx=list.get(n-1)[1];
      for(int i=n-2;i>=0;i--){
          long min2idx=list.get(i)[1];
          long min2=list.get(i)[0];
          ans2=Math.max(ans2, (minidx*min2idx)-(k*(min|min2)));
      }
      str.append(Math.max(ans, ans2)).append("\n");
  }

  public static void main(String[] args) throws java.lang.Exception {
    BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
    int q = Integer.parseInt(bf.readLine().trim());
    while(q-->0) {
        String s[]=bf.readLine().trim().split("\\s+");
        n=Integer.parseInt(s[0]);
        k=Integer.parseInt(s[1]);
        list=new ArrayList<>();
        s=bf.readLine().trim().split("\\s+");
        for(int i=0;i<n;i++) list.add(new long[]{Long.parseLong(s[i]), i+1});
        solve();
    }
    System.out.print(str);
  }
}