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 max(int x, int y) { return x > y ? x : y; }
int min(int x, int y) { return x < y ? x : y; }
int main() {
  ios_base::sync_with_stdio(0);
  int n, m;
  string s;
  cin >> n >> m;
  cin >> s;
  int u = 0;
  for (int i = n - 1; i > 0; --i) {
    if (s.substr(0, i) == s.substr(n - i, i)) {
      u = i;
      break;
    }
  }
  string c = s.substr(u, n - u);
  string ans = s;
  for (int i = 0; i < m - 1; ++i) {
    ans += c;
  }
  cout << ans << endl;
}