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;
  string t;
  cin >> n >> k >> t;
  int cnt = 1;
  int pos = 1;
  string ans = t;
  while (cnt < k) {
    if (pos >= int((ans).size())) {
      ans += t;
      ++cnt;
    } else {
      bool ok = true;
      int len = 0;
      for (int i = 0; i < int((t).size()); ++i) {
        if (pos + i >= int((ans).size())) break;
        ++len;
        if (ans[pos + i] != t[i]) ok = false;
      }
      if (ok) {
        ans += t.substr(len);
        ++cnt;
      }
    }
    ++pos;
  }
  cout << ans << endl;
  return 0;
}