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;
int n, k;
char a[51], b[10005];
int nxt[10005];
void getnxt() {
  nxt[0] = 0;
  int j = 1, k = 0;
  while (j < n) {
    if (a[j] == a[k]) {
      k++;
      nxt[j] = k;
      j++;
    } else {
      if (k > 0)
        k = nxt[k - 1];
      else {
        nxt[j] = k;
        j++;
      }
    }
  }
}
int main() {
  cin >> n >> k;
  scanf("%s", a);
  getnxt();
  for (int i = 0; i < k; i++) {
    if (i == 0)
      printf("%s", a);
    else
      printf("%s", a + nxt[n - 1]);
  }
  return 0;
}