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, prefix_array[60] = {0}, i = 1, j = 0, p = 0;
  char a[60], b[60];
  cin >> n;
  cin >> k;
  scanf("%s", a);
  while (1) {
    if (i >= n) break;
    if (j == 0 && a[j] != a[i]) {
      i++;
    } else if (j != 0 && a[j] != a[i]) {
      j = prefix_array[j - 1];
    } else if (a[j] == a[i]) {
      prefix_array[i] = j + 1;
      i++;
      j++;
    }
  }
  cout << a;
  for (i = prefix_array[n - 1]; i < n; i++) {
    b[p] = a[i];
    p++;
  }
  b[p] = '\0';
  for (i = 0; i < k - 1; i++) {
    cout << b;
  }
  cout << endl;
}