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>
char s[200];
int n, k;
bool check(int x) {
  for (int i = 1; i <= x; i++)
    if (s[i] != s[n - x + i]) return false;
  return true;
}
int main() {
  scanf("%d%d", &n, &k);
  scanf("%s", s + 1);
  int same = 0;
  for (int i = 1; i < n; i++)
    if (check(i)) same = i;
  if (same == n) same = n - 1;
  printf("%s", s + 1);
  for (int i = 1; i < k; i++)
    for (int i = same + 1; i <= n; i++) putchar(s[i]);
  puts("");
  return 0;
}