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.BufferedReader;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Main {

  public static void main(String[] args) throws Exception {
   Scanner sc = new Scanner(System.in) ;
   PrintWriter out = new PrintWriter(System.out);
    int tc = sc.nextInt();
    while (tc-- > 0) {
     int n = sc.nextInt(), k = sc.nextInt();
     char []s = sc.next().toCharArray();
     int longest = 0;
      for (int i = 0; i < (n - 1) / 2; i++) {
        if (s[i] == s[n - i - 1])
          longest++;
        else
          break;
      }

      if(longest >= k) {
        System.out.println("YES");
      } else{
        System.out.println("NO");
      }
    }
   out.flush();
  }


  static class Scanner {

    StringTokenizer st;
    BufferedReader br;

    public Scanner(InputStream s) {
      br = new BufferedReader(new InputStreamReader(s));
    }

    public String next() throws IOException {
      while (st == null || !st.hasMoreTokens()) {
        st = new StringTokenizer(br.readLine());
      }
      return st.nextToken();
    }

    public int nextInt() throws IOException {
      return Integer.parseInt(next());
    }

    public long nextLong() throws IOException {
      return Long.parseLong(next());
    }

    public String nextLine() throws IOException {
      return br.readLine();
    }

    public double nextDouble() throws IOException {
      String x = next();
      StringBuilder sb = new StringBuilder("0");
      double res = 0, f = 1;
      boolean dec = false, neg = false;
      int start = 0;
      if (x.charAt(0) == '-') {
        neg = true;
        start++;
      }
      for (int i = start; i < x.length(); i++) {
        if (x.charAt(i) == '.') {
          res = Long.parseLong(sb.toString());
          sb = new StringBuilder("0");
          dec = true;
        } else {
          sb.append(x.charAt(i));
          if (dec) {
            f *= 10;
          }
        }
      }
      res += Long.parseLong(sb.toString()) / f;
      return res * (neg ? -1 : 1);
    }

    public boolean ready() throws IOException {
      return br.ready();
    }
  }
}
