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 std::cerr;
using std::cin;
using std::cout;
using std::endl;
using std::make_pair;
using std::pair;
int main() {
  std::ios::sync_with_stdio(false);
  int n, k;
  cin >> n >> k;
  std::string s;
  cin >> s;
  int t = n + 1, len = n;
  for (int i = 1; i < len; ++i) {
    bool flag = true;
    for (int j = 0, k = len - i; j < i; ++j, ++k) {
      if (s[j] != s[k]) {
        flag = false;
        break;
      }
    }
    if (flag) t = i;
  }
  if (t == n + 1) {
    for (register int i = (1); i <= (k); ++i) cout << s;
    return 0;
  }
  std::string s_out = s.substr(t, n - t);
  cout << s;
  --t;
  for (register int i = (2); i <= (k); ++i) {
    cout << s_out;
  }
  return 0;
}