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;
void optimizeIO() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
}
int32_t main() {
  optimizeIO();
  long long tt = 1;
  while (tt--) {
    long long n, k;
    cin >> n >> k;
    string s;
    cin >> s;
    long long ind = 1;
    string pref;
    while (ind < n) {
      pref = s.substr(ind, n - ind);
      if (pref == s.substr(0, pref.size())) break;
      ind++;
    }
    string res = s;
    k--;
    while (k--) {
      res += s.substr(n - ind, ind);
    }
    cout << res;
  }
  return 0;
}