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, i, z, j = 1, t;
  string s;
  cin >> n >> k;
  cin >> s;
  cout << s;
  for (t = 1; t < s.length(); ++t) {
    z = 0;
    for (j = t; j < s.length(); ++j, z++)
      if (s[z] != s[j]) break;
    if (j == s.length()) break;
  }
  int an = s.length() - t;
  for (i = 1; i < k; ++i) {
    for (j = an; j < s.length(); ++j) cout << s[j];
  }
  cout << endl;
  return 0;
}