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, k;
  cin >> n >> k;
  string t;
  cin >> t;
  if (n == 1) {
    while (k--) {
      cout << t;
    }
  } else {
    int pos = 0;
    for (int i = 1; i < n; i++) {
      if (t[i] != t[0]) {
        continue;
      }
      for (int j = i; j < n; j++) {
        if (t[j] == t[j - i]) {
          pos++;
        } else {
          pos = 0;
          break;
        }
      }
      i = (pos > 0) ? i + pos - 1 : i;
    }
    cout << t;
    for (int i = 0; i < k - 1; i++) {
      for (int j = pos; j < n; j++) {
        cout << t[j];
      }
    }
  }
  cout << "\n";
  return 0;
}