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(NULL);
  int t = 1;
  while (t--) {
    int n, k;
    cin >> n >> k;
    string str;
    cin >> str;
    int pos = -1;
    for (int i = 1; i < n; i++) {
      int start = 0;
      for (int j = i; j < n; j++) {
        if (str[j] == str[start]) {
          start++;
        } else {
          start = 0;
          break;
        }
      }
      if (start != 0) {
        pos = i;
        break;
      }
    }
    string ans = str;
    if (pos != -1) {
      ans = str.substr(n - pos, pos);
    }
    cout << str;
    for (int i = 0; i < k - 1; i++) {
      cout << ans;
    }
  }
  return 0;
}