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, m;
char s[55];
int nnext[55];
void findnext() {
  nnext[0] = -1;
  int i = -1, j = 0;
  while (j < n) {
    if (i < 0 || s[i] == s[j])
      nnext[++j] = ++i;
    else
      i = nnext[i];
  }
}
int main() {
  cin >> n >> m;
  scanf("%s", s);
  findnext();
  int cnt = nnext[n];
  for (int i = 0; i < m; i++) {
    for (int j = 0; j < n - cnt; j++) {
      printf("%c", s[j]);
    }
  }
  for (int i = 0; i < cnt; i++) {
    printf("%c", s[i]);
  }
  puts("");
}