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;
  cin >> n >> k;
  string s;
  cin >> s;
  string t = "";
  while (k > 0) {
    for (int i = 0; i <= t.size(); i++) {
      if (i + n - 1 >= t.size()) {
        bool blogai = false;
        for (int j = i; j < t.size(); j++)
          if (t[j] != s[j - i]) blogai = true;
        if (!blogai) {
          for (int j = i; j <= i + n - 1; j++)
            if (j >= t.size()) t.push_back(s[j - i]);
          break;
        }
      }
    }
    k--;
  }
  cout << t << "\n";
}