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 n, k, i, q, num, tmp, T;
char s[100005];
int main() {
  scanf("%d%d%s", &n, &k, s + 1);
  for (int j = n; j > 1; j--) {
    i = 1;
    tmp = 0;
    q = j;
    if (s[1] == s[q]) {
      while (q <= n && s[i] == s[q]) {
        i++, q++, tmp++;
      }
    }
    if (tmp >= num && q == n + 1) num = tmp, T = j;
  }
  if (num == 0) {
    while (k--)
      for (int p = 1; p <= n; p++) printf("%c", s[p]);
    return 0;
  }
  for (int p = 1; p <= k; p++)
    for (int r = 1; r < T; r++) printf("%c", s[r]);
  for (int p = T; p <= n; p++) printf("%c", s[p]);
  return 0;
}