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>
const int maxn = 1000;
char str[maxn];
int f[maxn];
inline void getfail() {
  f[0] = f[1] = 0;
  for (int i = 1; str[i]; i++) {
    int j = f[i];
    while (j && str[j] != str[i]) j = f[j];
    f[i + 1] = str[i] == str[j] ? j + 1 : 0;
  }
}
int main() {
  int n, k;
  scanf("%d%d", &n, &k);
  scanf("%s", str);
  getfail();
  int len = strlen(str);
  printf("%s", str);
  k--;
  while (k--) {
    for (int i = f[len]; i < len; i++) {
      printf("%c", str[i]);
    }
  }
}