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() {
  long long n, k, i, l;
  cin >> n >> k;
  string s;
  cin >> s;
  long long max = 0;
  for (i = 1; i < n; i++) {
    long long temp = 0;
    for (l = 0; l < n; l++) {
      if (i + l < n) {
        if (s[i + l] == s[l]) {
          temp++;
        }
      } else
        break;
    }
    if (temp == n - i) {
      max = n - i;
      break;
    }
  }
  string ans = s;
  for (i = 1; i < k; i++) {
    ans += s.substr(max, n - max);
  }
  cout << ans;
  return 0;
}