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() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int TESTS = 1;
  while (TESTS--) {
    int n, k, i, j;
    string s;
    cin >> n >> k;
    cin >> s;
    if (n == 1) {
      for (i = 0; i < k; i++) cout << s;
      return 0;
    }
    for (i = 1; i < n; i++) {
      for (j = i; j < n; j++) {
        if (s[j] != s[j - i]) break;
      }
      if (j == n) break;
    }
    k--;
    cout << s;
    while (k--) {
      for (j = 0; j < i; j++) {
        cout << s[n - i + j];
      }
    }
  }
  return 0;
}