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.
//K-OS WITH THE OCDE

#pragma GCC optimize("Ofast")
#pragma GCC target("avx,avx2,fma")
#pragma GCC optimization ("unroll-loops")

#include <iostream>
#include <numeric>
#include <iomanip>
#include <cstdio>
#include <cstdlib>
#include <algorithm>
#include <cmath>
#include <vector>
#include <set>
#include <stack>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <queue>
#include <deque>
#include <ctime>
#include <cassert>
#include <complex>
#include <string>
#include <cstring>
#include <climits>

using namespace std;

typedef long long int ll;
typedef long double db;


#define TEST ll t; cin>>t; while(t--)
#define vell vector<ll>
#define pl pair<ll,ll>
#define all(v) v.begin(),v.end()
#define pb push_back
#define ff first
#define ss second
#define mp make_pair
#define dbg(x)  cerr << #x << ": "<< x <<endl
#define dbg2(x,y) cerr<< #x <<": "<< x <<" || "<< #y << ": " << y << endl

#define endl "\n"
#define MAX 1e18
#define MIN INT_MIN
#define mod 1000000007



void solve()
{
    string s;
    ll n, k;
    cin >> n >> k;
    cin >> s;
    ll i = 0;
    for (; i < k ; ++i) {
        if (s[i] != s[n - i - 1]) {
            cout << "NO" << endl;
            return;
        }
    }

    string ss = s.substr(i, n - 2 * k);
    if (ss.size())
        cout << "YES" << endl;
    else
        cout << "NO" << endl;
}

int main()
{
#ifndef ONLINE_JUDGE
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
#endif
    ios_base::sync_with_stdio(0); cin.tie(0);
    TEST
    solve();

    cerr << "[time:" << 1.0 * clock() / CLOCKS_PER_SEC << "s] " << endl;

}

