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;
  cin >> n >> k;
  string s;
  cin >> s;
  int l = s.length();
  int nn = s.length() - 1;
  while (nn > 0) {
    if (s.substr(0, nn) == s.substr(l - nn)) {
      string xx = s.substr(nn);
      cout << s;
      for (long long i = 1; i < k; i++) {
        cout << xx;
      }
      return 0;
    }
    nn--;
  }
  for (long long i = 0; i < k; i++) {
    cout << s;
  }
}