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;
const double PI = 2 * acos(0.0);
int main() {
  ios_base::sync_with_stdio(false), cin.tie(NULL);
  int n, k;
  cin >> n >> k;
  string s, ans = "", match = "", sub = "";
  cin >> s;
  ans += s, k--;
  for (int i = 1; i < s.length(); i++) {
    int pos = i;
    for (int j = 0; j < s.length(); j++) {
      if (s[pos] == s[j]) {
        pos++;
        continue;
      } else {
        break;
      }
    }
    if (pos == s.length()) {
      for (int d = i; d < s.length(); d++) {
        match += s[d];
      }
      break;
    }
  }
  for (int i = match.length(); i < s.length(); i++) {
    sub += s[i];
  }
  for (int i = 1; i <= k; i++) {
    ans += sub;
  }
  cout << ans << endl;
  return 0;
}