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<bits/stdc++.h>
using namespace std;
 
typedef long long ll;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<vi> vvi;
typedef vector<vl> vvl;
typedef pair<int,int> pii;
typedef pair<double, double> pdd;
typedef pair<ll, ll> pll;
typedef vector<pii> vii;
typedef vector<pll> vll;
typedef double dl;
 
#define PB push_back
#define F first
#define S second
#define MP make_pair
#define endl '\n'
#define all(a) (a).begin(),(a).end()
#define sz(x) (int)x.size()
#define mid(l,r) ((r+l)/2)
#define left(node) (node*2)
#define right(node) (node*2+1)
#define mx_int_prime 999999937
 
const double PI = acos(-1);
const double eps = 1e-9;
const int inf = 2000000000;
const ll infLL = 9000000000000000000;
#define MOD 1000000007
 
#define mem(a,b) memset(a, b, sizeof(a) )
#define gcd(a,b) __gcd(a,b)
#define sqr(a) ((a) * (a))
 
#define optimize() ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
#define fraction() cout.unsetf(ios::floatfield); cout.precision(10); cout.setf(ios::fixed,ios::floatfield);
#define file() freopen("input.txt","r",stdin);freopen("output.txt","w",stdout);
 
typedef vector<int>::iterator vit;
typedef set<int>::iterator sit;
 
 
int dx[] = {0, 0, +1, -1};
int dy[] = {+1, -1, 0, 0};
//int dx[] = {+1, 0, -1, 0, +1, +1, -1, -1};
//int dy[] = {0, +1, 0, -1, +1, -1, +1, -1};
 
 
 
template < typename F, typename S >
ostream& operator << ( ostream& os, const pair< F, S > & p ) {
            return os << "(" << p.first << ", " << p.second << ")";
}
 
template < typename T >
ostream &operator << ( ostream & os, const vector< T > &v ) {
            os << "{";
                for(auto it = v.begin(); it != v.end(); ++it) {
                                if( it != v.begin() ) os << ", ";
                                        os << *it;
                                            }
                    return os << "}";
}
 
template < typename T >
ostream &operator << ( ostream & os, const set< T > &v ) {
            os << "[";
                for(auto it = v.begin(); it != v.end(); ++it) {
                                if( it != v.begin() ) os << ", ";
                                        os << *it;
                                            }
                    return os << "]";
}
 
template < typename T >
ostream &operator << ( ostream & os, const multiset< T > &v ) {
            os << "[";
                for(auto it = v.begin(); it != v.end(); ++it) {
                                if( it != v.begin() ) os << ", ";
                                        os << *it;
                                            }
                    return os << "]";
}
 
template < typename F, typename S >
ostream &operator << ( ostream & os, const map< F, S > &v ) {
            os << "[";
                for(auto it = v.begin(); it != v.end(); ++it) {
                                if( it != v.begin() ) os << ", ";
                                        os << it -> first << " = " << it -> second ;
                                            }
                    return os << "]";
}
 
#define dbg(args...) do {cerr << #args << " : "; faltu(args); } while(0)
 
void faltu () {
            cerr << endl;
}
 
template <typename T>
void faltu( T a[], int n ) {
            for(int i = 0; i < n; ++i) cerr << a[i] << ' ';
                cerr << endl;
}
 
template <typename T, typename ... hello>
void faltu( T arg, const hello &... rest) {
            cerr << arg << ' ';
                faltu(rest...);
}
 
 
int main()
{
    optimize();
    ll t;
    cin>>t;
    while(t--)
    {
      ll n,k,c=0;
      cin>>n>>k;
      string s;
      cin>>s;
      if(sz(s)%2!=0){
      for(ll i=0,j=n-1;i<j;i++,j--)
      {
        if(s[i]==s[j])
        {
          c++;
        }
        else
        {
          break;
        }

      }
      }
      else{
      for(ll i=0,j=n-1;i<j;i++,j--)
      {
        if(n/2==j)break;
        if((n/2)-1==i)break;
        if(s[i]==s[j])
        {
          c++;
        }
        else
        {
          break;
        }

      }

      }
      if(c>=k)
      {
        cout<<"YES"<<endl;
      }
      else
      {
        cout<<"NO"<<endl;
      }
    }
 
    return 0;
}