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() {
  int n, k, l = 0;
  string t;
  cin >> n >> k >> t;
  for (int i = 1; i < t.size(); ++i) {
    if (t[i] == t[0]) {
      bool b = 1;
      for (long long j = i + 1; j < t.size(); ++j) {
        if (t[j] != t[j - i]) {
          b = 0;
          break;
        }
      }
      if (b) {
        l = t.size() - i;
        break;
      }
    }
  }
  cout << t;
  for (int i = 1; i < k; ++i) {
    for (long long j = l; j < t.size(); ++j) {
      cout << t[j];
    }
  }
  cout << endl;
  return 0;
}