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 s[55];
int Next[55];
void kmp_pre(char* pat) {
  int l = strlen(pat);
  int i = 0, j = -1;
  Next[0] = -1;
  while (i < l) {
    if (j == -1 || pat[i] == pat[j]) {
      i++;
      j++;
      Next[i] = j;
    } else {
      j = Next[j];
    }
  }
}
int main(void) {
  int n, k;
  scanf("%d%d", &n, &k);
  scanf("%s", s);
  kmp_pre(s);
  int cnt = Next[n];
  if (cnt == 0) {
    for (int i = 0; i < k; i++) {
      printf("%s", s);
    }
    printf("\n");
  } else {
    printf("%s", s);
    for (int i = 0; i < k - 1; i++) {
      printf("%s", s + cnt);
    }
    printf("\n");
  }
  return 0;
}