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 str;
int main() {
  cin >> n >> k;
  cin >> str;
  int index = 0;
  int size = 0;
  string ans;
  while (k) {
    bool flag = true;
    for (int i = 0; i + index < size; i++) {
      flag &= str[i] == ans[index + i];
    }
    if (flag) {
      int diff = n - (size - index);
      for (int i = 0; i < diff; i++) {
        ans += str[n - diff + i];
      }
      size += diff;
      k--;
    }
    index++;
  }
  cout << ans << endl;
}