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;
long long min(long long a, long long b) {
  if (a < b) return a;
  return b;
}
int main() {
  std::ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long long n, k;
  cin >> n >> k;
  string s;
  cin >> s;
  int ans = -1;
  for (int i = 1; i < s.length(); i++) {
    bool f = false;
    for (int j = 0; j < s.length() - i; j++) {
      if (s[i + j] != s[j]) {
        f = true;
        break;
      }
    }
    if (f == false) {
      ans = i;
      break;
    }
  }
  string a = s;
  if (ans == -1)
    for (int i = 0; i < k - 1; i++) a += s;
  else
    for (int i = 0; i < k - 1; i++) a += s.substr(s.length() - ans, ans);
  cout << a << endl;
  return 0;
}