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() {
  int n, k;
  scanf("%d %d", &n, &k);
  char a[55], b[3000];
  scanf("%s", a);
  memset(b, 0, sizeof(b));
  int e = 1;
  int i = 0;
  while (k) {
    int ok = 1;
    for (int j = 0; j < n; j++) {
      if (b[i + j] == a[j]) {
        continue;
      } else if (b[i + j] == 0) {
        b[i + j] = a[j];
      } else {
        ok = 0;
        break;
      }
    }
    i++;
    if (ok) k--;
  }
  printf("%s\n", b);
}