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() {
  int k, n, ch = 0;
  string s, g;
  cin >> n >> k >> s;
  for (int i = 1; i <= n && ch == 0; i++) {
    string t = s.substr(0, i);
    string temp = "\0";
    int count;
    (n % i == 0) ? count = n / i : count = (n / i) + 1;
    for (int j = 0; j < count; j++) temp += t;
    if (temp.find(s) == 0) {
      g = t;
      ch++;
    }
  }
  string l = "\0";
  for (int i = 0; i < k - 1; i++) l += g;
  l += s;
  cout << l << endl;
}