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() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int n, k, i, f = 0, j, m;
  cin >> n >> k;
  string s, tmp = "";
  cin >> s;
  for (i = 1; i < n; i++)
    if (s[i] != s[0]) break;
  if (i == n) {
    cout << s;
    for (i = 0; i < k - 1; i++) cout << s[0];
    return 0;
  }
  int size = 0, ok = 1;
  for (j = n - 1; j > 0; j--) {
    int x = 0;
    for (m = j, i = 0; m < n && i < n; m++, i++) {
      if (s[m] == s[i])
        x++;
      else {
        break;
      }
    }
    if (m == n) size = max(size, x);
  }
  for (i = size; i < n; i++) tmp += s[i];
  cout << s;
  for (i = 0; i < k - 1; i++) cout << tmp;
  return 0;
}