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);
  cin.tie(0);
  cout.tie(0);
  long long n, k;
  string t, s;
  cin >> n >> k >> t;
  long long i = 0, flag = 0;
  for (; i < n - 1; i++) {
    if (t.substr(0, n - 1 - i) == t.substr(i + 1, n - 1)) {
      flag = 1;
      break;
    }
  }
  string p = t.substr(0, n - 1 - i);
  string con = "";
  if (flag)
    con = t.substr(p.size(), n);
  else
    con = t;
  s = t;
  for (long long j = 0; j < k - 1; j++) s += con;
  cout << s << endl;
  return 0;
}