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>
#pragma warning(disable : 4996)
using namespace std;
char s[55];
int main() {
  int n, k, i, j, m, pos, flag;
  scanf("%d%d", &n, &m);
  scanf("%s", s);
  pos = 0;
  for (i = 1; i < n; i++) {
    if (s[i] == s[0]) {
      flag = 1;
      for (k = 1, j = i + 1; j < n; j++, k++) {
        if (s[j] != s[k]) flag = 0;
      }
      if (flag) {
        pos = n - i;
        break;
      }
    }
  }
  printf("%s", s);
  for (i = 1; i < m; i++) {
    for (j = pos; j < n; j++) printf("%c", s[j]);
  }
  printf("\n");
  return 0;
}