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() {
  string t, temp;
  int l, n;
  cin >> l >> n;
  cin >> t;
  for (int i = 1; i <= t.size(); i++) {
    int x = 1;
    for (int j = i; j < t.size(); j++) {
      if (t[j] != t[j - i]) {
        x = 0;
        break;
      }
    }
    if (x) {
      for (int k = t.size() - i; k < t.size(); k++) temp.push_back(t[k]);
      break;
    }
  }
  string ans = t;
  n--;
  while (n--) ans.append(temp);
  cout << ans;
  return 0;
}