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() {
  ios_base::sync_with_stdio(false);
  int n, k;
  cin >> n >> k;
  string t;
  cin >> t;
  vector<int> prefix(n, 0);
  for (int i = 1; i < n; i++) {
    int j = prefix[i - 1];
    while (j > 0 && t[i] != t[j]) {
      j = prefix[j - 1];
    }
    if (t[i] == t[j]) {
      j++;
    }
    prefix[i] = j;
  }
  int len = prefix[n - 1];
  string a = t.substr(len, n - len);
  string ans = t;
  for (int i = 0; i < k - 1; i++) {
    ans += a;
  }
  cout << ans;
}