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 nxt[55];
int n;
void getnext() {
  nxt[0] = -1;
  int k = -1;
  for (int i = 1; i < n; i++) {
    while (k != -1 && s[i] != s[k + 1]) k = nxt[k];
    if (s[i] == s[k + 1]) k++;
    nxt[i] = k;
  }
}
int main() {
  int k;
  scanf("%d%d", &n, &k);
  scanf("%s", s);
  getnext();
  for (int i = 0; i < n; i++) printf("%c", s[i]);
  for (int j = 1; j < k; j++)
    for (int p = nxt[n - 1] + 1; p < n; p++) printf("%c", s[p]);
  printf("\n");
  return 0;
}