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;
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long n, k;
  cin >> n >> k;
  string x;
  cin >> x;
  string ans = x;
  string y = "";
  long long p = n;
  for (long long i = 1; i < n; i++) {
    long long j;
    y = "";
    for (j = 0; i + j < n; j++) {
      if (x[i + j] != ans[j]) break;
      y += ans[j];
    }
    if (i + j == n) {
      p = i;
      break;
    }
  }
  p = n - p;
  while (p--) {
    ans.erase(ans.begin());
  }
  cout << x;
  while (--k) {
    cout << ans;
  }
  cout << endl;
}