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;
signed main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long q, a, b, c, d, e, f, n, i, j, t;
  cin >> n >> q;
  string s;
  cin >> s;
  bool check = 0;
  for (i = 1; i < n; ++i) {
    if (s[i] == s[0]) {
      e = 0;
      while (s[e] == s[i + e] && e + i < n) {
        if (e + i == n - 1) {
          check = 1;
          break;
        }
        e++;
      }
      if (check) {
        break;
      }
    }
  }
  cout << s;
  for (t = 1; t < q; ++t) {
    for (j = n - i; j < n; ++j) {
      cout << s[j];
    }
  }
}