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() {
  long long n, k, i, j, l, m;
  cin >> n >> k;
  string s;
  cin >> s;
  long long max, indx = 0, cnt = -1;
  for (i = 1; i < s.length(); i++) {
    if (s[i] == s[0]) {
      cnt = 1;
      for (j = i + 1; j < s.length(); j++) {
        if (s[j] != s[cnt]) {
          j = s.length();
        } else
          cnt++;
      }
      if (cnt >= indx && j == s.length()) indx = cnt;
    }
  }
  cout << s;
  k--;
  while (k > 0) {
    for (j = indx; j < s.length(); j++) cout << s[j];
    k--;
  }
  cout << endl;
}