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;
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  long long n, k, i;
  string s;
  cin >> n >> k;
  cin >> s;
  string ans = s;
  k--;
  for (i = 1; i < s.size(); i++) {
    if (s.substr(i) == s.substr(0, s.size() - i)) {
      while (k--) ans += s.substr(s.size() - i);
      cout << ans << endl;
      return 0;
    }
  }
  for (i = 0; i < k; i++) ans += s;
  cout << ans << endl;
}