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.


//@author->.....future_me......//

//..............Learning.........//

/*Compete against yourself*/

import java.util.*;
import java.io.*;
import java.lang.*;
import java.math.BigInteger;

public class A {

	static FastReader		sc	= new FastReader();
	static PrintWriter	out	= new PrintWriter(System.out);

	public static void main(String[] args) throws Exception {
//		try {
//
		int t = sc.nextInt();
		while (t-- > 0)
			A.go();
		out.flush();
//		} catch (Exception e) {
//			return;
//		}
	}

	static int							count	= 0;
	static HashSet<Integer>	set		= new HashSet<Integer>();

//>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Code Starts <<<<<<<<<<<<<<<<<<<<<<<<<<<<< //

	static void go() {
		int n=sc.nextInt();
		int k=sc.nextInt();
		String s=sc.next();
		if(k==0) {
			out.println("YES");
			return;
		}
		boolean f=false;
		if(n%2==0&&k==n/2) {
			out.println("NO");
			return;
		}
		String s1="";
		for(int i=0;i<k;i++) {
			s1=s1+s.charAt(i);
}
		String s2="";
		for(int i=n-1;i>n-1-k;i--) {
			s2=s2+s.charAt(i);
}
//		out.println(s1+" "+s2);
		if(s1.equals(s2)) {
			out.println("YES");
			return;
		}
		out.println("NO");
		
	
	}
	static boolean pal(String s) {
		int l=0;int r=s.length()-1;
		while(l<=r) {
			if(s.charAt(l)!=s.charAt(r)) {
				return false;
			}
			l++;
			r--;
		}
		return true;
	}
	

//>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Code Ends <<<<<<<<<<<<<<<<<<<<<<<<<<<<< //

	static BigInteger gcd(BigInteger a, BigInteger b) {
		if (b.equals(BigInteger.ZERO)) {
			return a;
		}return gcd(b, a.mod(b));
	}
	static int	prime[]	= new int[200005];
	static int	N				= 200005;
	static void sieve() {
	
		for(int i=0;i<N;i++) {
			prime[i]=i;
}
		for (int i = 2; i * i <= N; i++) {
			if (prime[i] == i) {
				prime[i]=i;
				for (int j = i; j < N; j += i) {
					prime[j] =i;
				}}}
	}


	static int gcd(int a, int b) {
		if (b == 0) {
			return a;
		}return gcd(b, a % b);
	}
	 static void sort(int[] a) {
		ArrayList<Integer> aa = new ArrayList<>();
		for (Integer i : a) {
			aa.add(i);	}
		Collections.sort(aa);
		for (int i = 0; i < a.length; i++)
			a[i] = aa.get(i);}
	static void sort(long[] a) {
		ArrayList<Long> aa = new ArrayList<>();
		for (Long i : a) {
			aa.add(i);}
		Collections.sort(aa);
		for (int i = 0; i < a.length; i++)
			a[i] = aa.get(i);
	}

	static int mod = (int) 1e9 + 7;

	static long pow(long x, long y) {
		long res = 1l;
		while (y != 0) {
			if (y % 2 == 1) {
				res = (x * res);
				}	y /= 2;x = (x * x);
		}
		return res;
	}


//>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Fast IO <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< //

	static class FastReader {
		BufferedReader	br;
		StringTokenizer	st;
		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}		String next() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}		}	return st.nextToken();
		}	int nextInt() {
			return Integer.parseInt(next());
		}	long nextLong() {
			return Long.parseLong(next());
		}	double nextDouble() {
			return Double.parseDouble(next());
		}		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}	}}

class cell implements Comparable<cell>{
	long x;int ind;
	cell(long x,int ind){
		this.x=x;this.ind=ind;
	}
	@Override
	public int compareTo(cell o) {
		return -Long.compare(o.x, this.x);
	}
}