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 <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <queue>
#include <vector>
#include <deque>
#include <bitset>
#include <map>
#include <string>
using namespace std;
#define lowbit(x) x&-x
#define ll long long
#define dob double
#define For(i,s,n) for(ll i = s;i <= n;i++)
#define mem0(a) memset(a,0,sizeof a)
#define gcd(a,b) __gcd(a,b)
const int N = 150;
const double eps = 1e-6;
const ll mod = 998244353;
const int inf = 0x3f3f3f3f;
const int maxn = 1e4+50;
void read(int &res){
    char c;bool flag = true;
    while((c=getchar())<'0'||c>'9')if(c=='-')flag=-1;res=c-'0';
    while((c=getchar())>='0'&&c<='9')res=res*10+c-'0';res*=flag;
}
int t;
char s[N];
int main() {
    ios::sync_with_stdio(false);
    cout.tie(NULL);
    int t;
    cin>>t;
    while(t--){
        int n,k;
        cin>>n>>k;
        For(i,1,n) cin>>s[i];
        int l;
        if(n%2 == 0) l = n/2-1;
        else l = n/2;
        int cnt = 0;
        for(int i = 1,j = n;i <= l;i++,j--){
            if(i == l) cnt = l;
            if(s[i] != s[j]){
                cnt = i-1;
                break;
            }
        }
        if(cnt >= k) cout<<"YES"<<endl;
        else cout<<"NO"<<endl;
    }
    return 0;
}