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 n, m;
char ch[55];
int main() {
  scanf("%d%d", &n, &m);
  scanf("%s", ch);
  int poi = n;
  for (int i = 1; i < n; i++) {
    if (poi < n) {
      break;
    }
    for (int j = 0; i + j < n; j++) {
      if (ch[j] != ch[i + j]) {
        break;
      }
      if (i + j == n - 1) {
        poi = i;
      }
    }
  }
  for (int i = 1; i < m; i++) {
    for (int j = 0; j < poi; j++) {
      printf("%c", ch[j]);
    }
  }
  printf("%s", ch);
  return 0;
}