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[60];
int n, m, nex[60];
int main() {
  scanf("%d%d", &n, &m);
  scanf("%s", s + 1);
  int k = 0;
  for (int i = 2; i <= n; i++) {
    while (k && s[k + 1] != s[i]) k = nex[k];
    if (s[k + 1] == s[i]) k++;
    nex[i] = k;
  }
  for (int i = 1; i <= m; i++) {
    for (int j = 1; j <= n - nex[n]; j++) {
      printf("%c", s[j]);
    }
  }
  for (int i = n - nex[n] + 1; i <= n; i++) {
    printf("%c", s[i]);
  }
  return 0;
}