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, m;
string s;
int main() {
  cin >> n >> m;
  cin >> s;
  string t = "";
  for (int i = s.size() - 1; i >= 0; i--) {
    bool flg = true;
    reverse(t.begin(), t.end());
    t += s[i];
    reverse(t.begin(), t.end());
    string j = s + t;
    for (int z = j.size() - 1, q = s.size() - 1, c = 0; c < s.size();
         z--, q--, c++) {
      if (s[q] != j[z]) {
        flg = false;
        break;
      }
    }
    if (flg) break;
  }
  m--;
  cout << s;
  while (m--) {
    cout << t;
  }
  return 0;
}