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>
int main() {
  int n, k;
  scanf("%d %d", &n, &k);
  char a[100];
  scanf("%s", a);
  int w = 1, b = n;
  for (int i = 1; i < n; i++) {
    w = 1;
    for (int u = i, j = 0; u < n; u++, j++) {
      if (a[u] != a[j]) {
        w = 0;
        break;
      }
    }
    if (w) {
      b = i;
      break;
    }
  }
  printf("%s", a);
  for (int i = 0; i < k - 1; i++) {
    for (int u = n - b; u < n; u++) {
      printf("%c", a[u]);
    }
  }
}