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 t;
  cin >> t;
  for (int i = n - 2; i >= 0; i--) {
    string s1 = t.substr(0, i + 1);
    string s2 = t.substr(n - i - 1, i + 1);
    if (s1 == s2) {
      string t1 = t.substr(i + 1, n - i - 1);
      for (int j = 0; j < k - 1; j++) t = t + t1;
      cout << t << endl;
      return 0;
    }
  }
  for (int i = 0; i < k; i++) cout << t;
  cout << endl;
  return 0;
}