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 inf = 0x3f3f3f3f;
string sub(string a) {
  for (int i = 1; i < a.size(); i++) {
    if (a.substr(i, a.size() - 1) == a.substr(0, a.size() - i))
      return a.substr(a.size() - i, a.size());
  }
  return a;
}
int main() {
  int n, k;
  cin >> n >> k;
  string a, s;
  cin >> a;
  s = a;
  a = sub(a);
  for (int i = 1; i < k; i++) s += a;
  cout << s << endl;
  return 0;
}