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.

if __name__ == '__main__':
    cases=int(input())
    resultados=[]
    for c in range(cases):
        data = input().split()
        lenOfString = int(data[0])
        k=int(data[1])
        strinToEval=input()
        splitIt=True
        if(k==0):
            resultados.append("YES")
        elif((2*k+1)<=lenOfString):
            half=int(lenOfString/2)
            if(lenOfString%2==0):
                --half
            for h in range(half):
                if strinToEval[h]!=strinToEval[lenOfString-h-1]:
                    if(h<k):
                        resultados.append("NO")
                        splitIt=False
                    break
            if(splitIt):
                resultados.append("YES")
        else:
            resultados.append("NO")
    for r in resultados:
        print(r)



