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

public class Main {
    
    public static void main(String[] args) throws IOException {
        Scanner scn = new Scanner(System.in);
        OutputWriter out = new OutputWriter(System.out);
        // Always print a trailing "\n" and close the OutputWriter as shown at the end of your output
        
        // example:
        int t=scn.nextInt();
        for(int i1=0;i1<t;i1++){
            int n=scn.nextInt();
            long k=scn.nextInt();
            long[] a=new long[n+1];
            for(int i=1;i<=n;i++){
                a[i]=scn.nextInt();
            }
            long ans=Integer.MIN_VALUE;
            for(int i=n;i>=Math.max(1,n-201);i--){
                for(int j=i-1;j>=Math.max(1,n-201);j--){
                    long val=(long)(i)*j-k*(a[i]|a[j]);
                    if(val>ans){
                        ans=val;
                    }
                }
            }
            out.print(Long.toString(ans)+"\n");
        }
        
        out.close();
    }

    // fast input
    static class Scanner {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public Scanner(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream));
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    String line = reader.readLine();
                    if (line == null)
                        return null;
                    tokenizer = new StringTokenizer(line);
                } catch (Exception e) {
                    throw(new RuntimeException());
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() { return Integer.parseInt(next()); }
        public long nextLong() { return Long.parseLong(next()); }
        public double nextDouble() { return Double.parseDouble(next()); }
    }

    // fast output
    static class OutputWriter {
        BufferedWriter writer;

        public OutputWriter(OutputStream stream) {
            writer = new BufferedWriter(new OutputStreamWriter(stream));
        }

        public void print(int i) throws IOException { writer.write(i); }
        public void print(String s) throws IOException { writer.write(s); }
        public void print(char[] c) throws IOException { writer.write(c); }
        public void close() throws IOException { writer.close(); }
    }


}
