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.
#include <bits/stdc++.h>
#define rf freopen("input.txt","r",stdin);
#define wf freopen("output.txt","w",stdout);
#define test() int t1 ;cin>>t1; while(t1--)
using namespace std ;

void syswrite(){
    #ifndef ONLINE_JUDGE
    rf;wf;
    #endif
}


void code(){
    // your code 
    int n1,n2;
    string s1;
    cin>>n1>>n2>>s1;
    bool ans=1,ans1=0;

    for(int i=0;i<n2 and ans;i++){
        if(s1[i]!=s1[s1.length()-1 -i]){
            ans=0;
        }
    }

    if(2*n2 < s1.length()){
        ans1=1;
    }

    if(n2==0){
        ans=1;
    }


    if (ans and ans1){
        cout<<"YES"<<endl;
    }
    else{
        cout<<"NO"<<endl ;
    }
    
}

int main(void)
{   //syswrite();
    test(){
        code();
    }
}