1496_A. Split it!
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.
```python
from os import path
import sys,time
# mod = int(1e9 + 7)
# import re
from math import ceil, floor,gcd,log,log2 ,factorial,sqrt
from collections import defaultdict ,Counter , OrderedDict , deque
from itertools import combinations ,accumulate
# from string import ascii_lowercase ,ascii_uppercase
from bisect import *
from functools import reduce
from operator import mul
star = lambda x: print(' '.join(map(str, x)))
grid = lambda  r :[lint() for i in range(r)]
stpr = lambda x : sys.stdout.write(f'{x}' + '\n')
INF = float('inf')
if (path.exists('input.txt')):
    sys.stdin=open('input.txt','r');sys.stdout=open('output.txt','w');
import sys
from sys import stdin, stdout
from collections import *
from math import gcd, floor, ceil
def st(): return list(stdin.readline().strip())
def inp():
    return int(stdin.readline())
def inlt():
    return list(map(int, stdin.readline().split()))
def insr():
    s = input()
    return(list(s[:len(s) - 1]))
def invr():
    return map(int, stdin.readline().split())
def pr(n): return stdout.write(str(n)+"\n")


def solve():
	n,k = invr()
	s=input()
	l = 0
	r = len(s)-1
	while r>l and k>0:
		if s[l]==s[r]:
			l+=1
			r-=1
			k-=1
		else:
			break
	if r>=l:
		k = k-1
	if k<0:
		print('YES')
	else:
		print('NO')

	'''if s==s[::-1]:
		print('NO')
	else:
		print('YES')'''


t = 1
t = inp()
for _ in range(t):
    solve()


   

```