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 n, k;
  cin >> n >> k;
  string t;
  cin >> t;
  int c = 0, st = 0, f = 0;
  for (int i = 1; i < n; ++i) {
    c = 0;
    st = 0;
    int j = i;
    while (1) {
      if (t[j] == t[st]) {
        ++c;
        ++st;
        ++j;
      } else
        break;
      if (j == n) {
        f = 1;
        break;
      }
    }
    if (f == 1) break;
  }
  cout << t;
  --k;
  string s;
  for (int i = c; i < n; ++i) s.push_back(t[i]);
  while (k > 0) {
    cout << s;
    --k;
  }
}