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;
char s[55];
int main() {
  int n, m;
  scanf("%d%d", &n, &m);
  scanf("%s", s + 1);
  int len = strlen(s + 1);
  char ed = s[len];
  int Max = 0;
  for (int i = 1; i < len; i++) {
    if (s[i] == ed) {
      int r = len - 1, flag = true;
      for (int j = i - 1; j >= 1; j--) {
        if (s[j] != s[r]) {
          flag = false;
          break;
        }
        r--;
      }
      if (flag) Max = max(Max, i);
    }
  }
  printf("%s", s + 1);
  for (int i = 1; i < m; i++) {
    for (int j = Max + 1; j <= len; j++) printf("%c", s[j]);
  }
}