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 sys
import os
import math
import copy
from bisect import bisect
from io import BytesIO, IOBase
from math import sqrt,floor,factorial,gcd,log,ceil
from collections import deque,Counter,defaultdict
from itertools import permutations,combinations,accumulate

def Int():               return int(sys.stdin.readline())
def Mint():              return map(int,sys.stdin.readline().split())
def Lstr():              return list(sys.stdin.readline().strip())
def Str():               return sys.stdin.readline().strip()
def Mstr():              return map(str,sys.stdin.readline().strip().split())
def List():              return list(map(int,sys.stdin.readline().split()))
def Hash():              return dict()
def Mod():               return 1000000007
def Mat2x2(n):           return [List() for _ in range(n)]
def Lcm(x,y):            return (x*y)//gcd(x,y)
def dtob(n):             return bin(n).replace("0b","")
def btod(n):             return int(n,2) 
def watch(x):            return print(x)
def common(l1, l2):      return set(l1).intersection(l2)
def Most_frequent(list): return max(set(list), key = list.count)

def check(s):
     n=len(s)
     if(len(s)==1):
          return True
     for i in range(n//2):
          if(s[i]!=s[n-i-1]):
               return False
     return True
     
   
def solution():
     for _ in range(Int()):
          n,k=Mint()
          s=Lstr()
          a=0
          for i in range(k):
               if(s[i]!=s[n-i-1]):
                    a=1
                    break
          if(a==0 and k<=(n-1)//2):
               print("YES")
          else:
               print("NO")
                    
                         
               
               
               
               
          
               
if __name__ == "__main__":
     solution()