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;
string solve(int N, int K, const string& s) {
  int border = 0;
  for (int i = 1; i < N; ++i) {
    bool ok = true;
    for (int j = 0; j < i; ++j)
      if (s[j] != s[N - i + j]) {
        ok = false;
        break;
      }
    if (ok) border = i;
  }
  auto b = s.substr(border), ans = s;
  while (--K) ans += b;
  return ans;
}
int main() {
  ios::sync_with_stdio(false);
  int N, K;
  string s;
  cin >> N >> K >> s;
  auto ans = solve(N, K, s);
  cout << ans << '\n';
  return 0;
}