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;
int main() {
  int n, m;
  char s[60];
  cin >> n >> m;
  cin >> s;
  for (int i = 1; i < n; i++) {
    bool t = true;
    if (s[i] == s[0])
      ;
    {
      int j = i, k;
      for (k = 0; j < n; j++, k++) {
        if (s[k] != s[j]) {
          t = false;
          break;
        }
      }
      if (t) {
        cout << s;
        for (int a = 0; a < m - 1; a++) {
          for (int ss = k; ss < n; ss++) cout << s[ss];
        }
        cout << endl;
        return 0;
      }
    }
  }
  for (int a = 0; a < m; a++) cout << s;
  cout << endl;
  return 0;
}