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;
void prefix(string tt, int m, vector<int>& jj) {
  for (int i = 1; i < m; ++i) {
    int j = jj[i - 1];
    while (j > 0 && tt[i] != tt[j]) {
      j = jj[j - 1];
    }
    if (tt[i] == tt[j]) ++j;
    jj[i] = j;
  }
}
int main() {
  int n, k;
  string t;
  cin >> n >> k;
  cin >> t;
  vector<int> ff(n);
  int _size = t.size();
  prefix(t, _size, ff);
  int a = ff[n - 1];
  cout << t;
  for (int i = 0; i < k - 1; ++i) {
    for (int i = a; i < _size; ++i) cout << t[i];
  }
}