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 Q1
{
    public static void main(String args[])
    {
         try
         {
                BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
                StringTokenizer st= new StringTokenizer(br.readLine());
                String str;
                int cases=Integer.parseInt(st.nextToken(" "));//next token based on delimeter
                int ar[]=new int[cases];
                for(int i=1;i<=cases;i++)
                {
                    st= new StringTokenizer(br.readLine());
                    int l=Integer.parseInt(st.nextToken(" "));//next token based on delimeter
                    int k=Integer.parseInt(st.nextToken(" "));//next token based on delimeter
                    str= br.readLine().trim();
                    ar[i-1]=1;
                    if(2*k<l)
                        for(int j=0;j<k;j++)
                        {
                            if(str.charAt(j)!=str.charAt(l-1-j))
                            {
                                ar[i-1]=0;
                                break;
                            }
                        }
                    else
                        ar[i-1]=0;
                }
                
                for(int i=1;i<=cases;i++)
                {
                   if(ar[i-1]==0)
                      System.out.println("NO");
                   else
                      System.out.println("YES");
                }
        }
         
        catch(Exception e)
        {
            System.out.print("Error : "+e.getMessage());
        }
        finally
        {
            ;
        }
    }
}