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 n, k;
string s;
int main() {
  cin >> n >> k;
  cin >> s;
  int slen = s.length();
  int post = 0;
  for (int i = 1; i < n; i++) {
    bool same = true;
    for (int j = i; j < n; j++) {
      if (s[j] != s[j - i]) {
        same = false;
        break;
      }
    }
    if (same) {
      post = max(post, n - i);
    }
  }
  if (post == 0) {
    for (int i = 0; i < k; i++) {
      cout << s;
    }
    cout << "\n";
  } else {
    cout << s;
    for (int i = 0; i < (k - 1); i++) {
      for (int j = post; j < n; j++) {
        cout << s[j];
      }
    }
    cout << "\n";
  }
}