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 main() {
  char t[51];
  int n, k;
  int i, j;
  int lb = 0, ub = 0;
  int lf, uf = 0;
  scanf("%d %d %s", &n, &k, t);
  while (lb + ub < n) {
    ub = 0;
    while (lb < n && t[++lb] != t[0])
      ;
    while (lb + ++ub < n && t[ub + lb] == t[ub])
      ;
  }
  for (i = 0; i < k; i++) {
    for (j = 0; j < lb; j++) {
      printf("%c", t[j]);
    }
  }
  for (i = lb; i < n; i++) {
    printf("%c", t[i]);
  }
  return 0;
}