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;
char a[2000];
int n, k;
int main() {
  scanf("%d %d", &n, &k);
  scanf("%s", a + 1);
  int i, len = 0;
  for (i = n - 1; i >= 1; i--) {
    bool flag = true;
    for (int j = 1, p = n - i + 1; j <= i; j++, p++) {
      if (a[j] != a[p]) {
        flag = false;
        break;
      }
    }
    if (flag) {
      len = i;
      break;
    }
  }
  if (len == 0) {
    for (int i = 1; i <= k; i++)
      for (int j = 1; j <= n; j++) printf("%c", a[j]);
  } else {
    for (int j = 1; j <= n; j++) printf("%c", a[j]);
    for (int i = 1; i <= k - 1; i++)
      for (int j = len + 1; j <= n; j++) printf("%c", a[j]);
  }
  printf("\n");
  return 0;
}