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>
int main() {
  long n, k;
  std::cin >> n >> k;
  std::string s;
  std::cin >> s;
  long start(0);
  for (long dist = 1; dist < s.size(); dist++) {
    long g(dist);
    while (g < s.size()) {
      if (s[g - dist] != s[g]) {
        break;
      }
      ++g;
    }
    if (g == s.size()) {
      start = s.size() - dist;
      break;
    }
  }
  std::cout << s;
  for (long p = 1; p < k; p++) {
    std::cout << s.substr(start);
  }
  std::cout << std::endl;
  return 0;
}