Kawashiro Nitori is a girl who loves competitive programming.

One day she found a string and an integer. As an advanced problem setter, she quickly thought of a problem.

Given a string s and a parameter k, you need to check if there exist k+1 non-empty strings a_1,a_2...,a_{k+1}, such that $$$s=a_1+a_2+… +a_k+a_{k+1}+R(a_k)+R(a_{k-1})+…+R(a_{1}).$$$ 

Here + represents concatenation. We define R(x) as a reversed string x. For example R(abcd) = dcba. Note that in the formula above the part R(a_{k+1}) is intentionally skipped.

Input

The input consists of multiple test cases. The first line contains a single integer t (1≤ t≤ 100) — the number of test cases. The description of the test cases follows.

The first line of each test case description contains two integers n, k (1≤ n≤ 100, 0≤ k≤ ⌊ n/2 ⌋) — the length of the string s and the parameter k.

The second line of each test case description contains a single string s of length n, consisting of lowercase English letters.

Output

For each test case, print "YES" (without quotes), if it is possible to find a_1,a_2,…,a_{k+1}, and "NO" (without quotes) otherwise.

You can print letters in any case (upper or lower).

Example

Input


7
5 1
qwqwq
2 1
ab
3 1
ioi
4 2
icpc
22 0
dokidokiliteratureclub
19 8
imteamshanghaialice
6 3
aaaaaa


Output


YES
NO
YES
NO
YES
NO
NO

Note

In the first test case, one possible solution is a_1=qw and a_2=q.

In the third test case, one possible solution is a_1=i and a_2=o.

In the fifth test case, one possible solution is a_1=dokidokiliteratureclub.
import java.io.File;
import java.io.FileNotFoundException;
import java.util.Arrays;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Scanner;

public class Main {
    static Scanner in = new Scanner(System.in);

    // static Scanner in = new Scanner( new File("javain.txt"));
    public static void main(String[] args) throws FileNotFoundException {
        if(args.length > 0){
			in = new Scanner( new File("in.txt"));
		}
		int t = in.nextInt();
        for(int i = 0; i < t; i++){
            solve();
        }
    }

    public static void solve(){
		int n = in.nextInt();
		int k = in.nextInt();
		in.nextLine();
		String s = in.nextLine();
		
		int l = 0, r = n - 1;
		while(l < r && s.charAt(l) == s.charAt(r)){
			l ++;
			r --;
		}
		if(l > r){
			l -- ;
		}
		if(l >= k){
			System.out.println("YES");
			return ;
		}
		System.out.println("NO");
	}
}
