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 n, m, pos = 0;
string s;
int main() {
  scanf("%d%d", &n, &m);
  cin >> s;
  int len = s.size();
  n = len;
  pos = 0;
  for (int i = 1; i < len; i++) {
    if (s.substr(0, i) == s.substr(n - i, i)) pos = i;
  }
  for (int k = 2; k <= m; k++) {
    for (int i = pos; i < len; i++) {
      s = s + s[i];
    }
  }
  cout << s;
  return 0;
}