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;
const long long int N = 1e6 + 100;
long long int n, sol, m, k;
string str, ans;
int main(int argc, char** argv) {
  cin >> n >> m >> str;
  ans = str;
  for (int i = n - 1; i > 0; i--) {
    if (str[i] == str[0]) {
      int j = i, k = 0;
      for (; j < n; j++, k++)
        if (str[j] != str[k]) break;
      if (j == n) sol = k;
    }
  }
  for (int i = 1; i < m; i++) {
    for (int j = sol; j < n; j++) {
      ans += str[j];
    }
  }
  cout << ans;
  return 0;
}