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.*;
import java.util.*;

public class test1 {
	
	

	public static void main(String[] args) throws IOException{
//		BufferedReader bf = new BufferedReader(new FileReader("reduce.in"));
//		PrintWriter out = new PrintWriter(new BufferedWriter(new FileWriter("reduce.out")));
		BufferedReader bf =new BufferedReader(new InputStreamReader(System.in));
		
		
		int n = Integer.parseInt(bf.readLine());
	    int length = 0;
	    int k = 0;
	    String s = "";
	    for (int i = 0; i < n; i++){
	        StringTokenizer st = new StringTokenizer(bf.readLine());
	        length = Integer.parseInt(st.nextToken());
	        k = Integer.parseInt(st.nextToken());
	        st = new StringTokenizer(bf.readLine());
	        s = st.nextToken();
	        boolean ok = true;
	        for (int j = 0; j < k; j++) {
	        	if (s.charAt(j) == s.charAt(length-j-1)) {
	        		ok = true;
	        	}
	        	else {
	        		ok = false;
	        		break;
	        	}
	        }

	      if (length == 2*k){
	        System.out.println("NO");
	      }
	      else if (k == 0){
	        System.out.println("YES");
	      }
	      else if (ok){
	        System.out.println("YES");
	      }
	      else {
	    	  System.out.println("NO");
	      }


	    }

		
//		bf.close();
//		out.close();
	}
}