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>
const int maxn = 55;
char s[maxn];
int n, k;
void solve() {
  bool f = true;
  for (int i = 1; i < n; i++) {
    if (s[i] != s[0]) {
      f = false;
      break;
    }
  }
  if (f) {
    printf("%s", s);
    k--;
    while (k--) putchar(s[0]);
    puts("");
    return;
  }
  int l;
  for (l = n - 1; l >= 0; l--) {
    bool f = true;
    for (int i = 0; i < l; i++)
      if (s[i] != s[n - l + i]) {
        f = false;
        break;
      }
    if (f) break;
  }
  printf("%s", s);
  k--;
  l = n - l;
  while (k--)
    for (int i = n - l; i < n; i++) putchar(s[i]);
  puts("");
}
int main() {
  scanf("%d %d %s", &n, &k, s);
  solve();
  return 0;
}