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 second;
int a[(int)2e5 + 3];
int main() {
  ios::sync_with_stdio(false);
  cin >> N >> k >> second;
  string ans = second;
  k--;
  while (k--) {
    bool found = 0;
    int j = second.size() - 1;
    while (j-- >= 0) {
      int h = j;
      for (int i = ans.size() - 1; h >= 0; h--, i--) {
        if (ans[i] != second[h]) break;
      }
      if (h == -1) {
        for (int i = j + 1; i < second.size(); i++) ans += second[i];
        found = 1;
        break;
      }
    }
    if (!found) ans += second;
  }
  cout << ans;
  return 0;
}