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;
vector<int> prefixFunction(string s) {
  vector<int> p(s.size());
  int j = 0;
  for (int i = 1; i < (int)s.size(); i++) {
    while (j > 0 && s[j] != s[i]) j = p[j - 1];
    if (s[j] == s[i]) j++;
    p[i] = j;
  }
  return p;
}
int main() {
  int n, k;
  cin >> n >> k;
  string s;
  cin >> s;
  vector<int> v = prefixFunction(s);
  int ans = n - v[n - 1];
  for (typename decay<decltype(k - 1)>::type i = 0; i < k - 1; i++)
    cout << s.substr(0, ans);
  cout << s << '\n';
}