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() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int TESTS = 1;
  while (TESTS--) {
    long long n, k;
    cin >> n >> k;
    string t;
    cin >> t;
    string s = t;
    long long i = 1, flag = 0;
    while (i < n) {
      long long k = i;
      flag = 0;
      long long a = 0;
      while (k < n && s[k] == t[a]) {
        k++;
        a++;
        if (k == n) {
          flag = 1;
          break;
        }
      }
      if (flag == 1) break;
      i++;
    }
    for (long long int c = 1; c < k; c++) {
      s += t.substr(n - i, i);
    }
    cout << s;
  }
  return 0;
}