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.
// o daj okreni...
#include <bits/stdc++.h>
#define ll long long
#define pb push_back
#define xx first
#define yy second
#define all(x) x.begin(),x.end()
#define rall(x) x.rbegin(),x.rend()
#define sz(x) x.size()
#define pii pair<int,int>
#define en '\n'
#define sp ' '
#define ckmin(a, b) a = min(a, b)
#define ckmax(a, b) a = max(a, b)
#define ar array
#define ri(n) int n;cin>>n;
#define rl(n) ll n;cin>>n;
#define rs(n) string n;cin>>n;
#define rv(a) for(int i=0;i<a.size();i++)cin>>a[i];
#define yes cout<<"YES\n";
#define no cout<<"NO\n";
#define bitcnt(x) __builtin_popcount(x)
using namespace std;
//const ll mod = 998244353;
const ll mod = 1e9+7;
const int N = 2e5 + 2;
const int M = 1e6 + 2;
const int inf = 2e9;
const ll linf = 9e18;
void solve() {
    ri(n);
    ri(k);
    rs(s);
    int i = 0, j = n-1;
    int cnt = 0;
    while(i<j){
        if(s[i]==s[j]){
            cnt++;
            i++;
            j--;
        }
        else break;
    }
    if(cnt>k||(cnt==k&&i<=j))yes
    else no
}
int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    cerr.tie(0);
    ri(t);
    while(t--)solve();
    return 0;
}
