Problem: You are given a string t consisting of n lowercase Latin letters and an integer number k.

Let's define a substring of some string s with indices from l to r as s[l ... r].

Your task is to construct such string s of minimum possible length that there are exactly k positions i such that s[i ... i + n - 1] = t. In other words, your task is to construct such string s of minimum possible length that there are exactly k substrings of s equal to t.

It is guaranteed that the answer is always unique.

Input

The first line of the input contains two integers n and k (1 ≤ n, k ≤ 50) — the length of the string t and the number of substrings.

The second line of the input contains the string t consisting of exactly n lowercase Latin letters.

Output

Print such string s of minimum possible length that there are exactly k substrings of s equal to t.

It is guaranteed that the answer is always unique.

Examples

Input

3 4
aba


Output

ababababa


Input

3 2
cat


Output

catcat

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
priority_queue<pair<int, int>, vector<pair<int, int> >,
               greater<pair<int, int> > >
    q;
vector<int> v;
int main() {
  int n, m;
  cin >> n >> m;
  string s, second, xx, yy;
  cin >> s;
  second = s;
  for (int i = 1; i < int(s.size()); i++) {
    xx = s.substr(i, n - 1);
    yy = s.substr(0, n - i);
    if (xx == yy) {
      second = s.substr(int(yy.size()), n - 1);
      break;
    }
  }
  cout << s;
  for (int i = 2; i <= m; i++) cout << second;
  cout << endl;
}