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 main() {
  int n, k, p = 0, i, j;
  cin >> n >> k;
  string s, st;
  cin >> s;
  st = "";
  for (i = 0; i < n - 1; i++) {
    st += s[i];
    if (s.substr(n - 1 - i, i + 1) == st) {
      p = i + 1;
    }
  }
  string ans = "";
  ans += s;
  for (i = 0; i < k - 1; i++) {
    ans += s.substr(p, n - p);
  }
  cout << ans;
}