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;
string s;
bool check(string ss) {
  int cnt = 0;
  for (int i = 0; i < ss.size(); i++) {
    string curr = "";
    for (int j = i; j < i + n; j++) {
      if (i + n > ss.size()) break;
      curr += ss[j];
    }
    if (curr == s) cnt++;
  }
  return cnt == k;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> k;
  cin >> s;
  string ans = "";
  for (int i = 0; i < k; i++) {
    ans += s;
  }
  for (int i = 0; i < n; i++) {
    string news = s;
    for (int j = 0; j < k - 1; j++) {
      for (int a = i; a < n; a++) {
        news += s[a];
      }
    }
    if (check(news)) {
      if (news.size() < ans.size()) ans = news;
    }
  }
  cout << ans << '\n';
  return 0;
}