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;
  string s;
  cin >> n >> k >> s;
  int ans = 0;
  for (int i = n - 1; i > 0; i--) {
    int flag = 1;
    for (int j = 0; j < int(i); ++j) {
      if (s[j] != s[n - i + j]) {
        flag = 0;
        break;
      }
    }
    if (flag) {
      ans = i;
      break;
    }
  }
  string anss = s;
  while (k > 1) {
    for (int i = 0; i < int(n - ans); ++i) {
      anss += s[ans + i];
    }
    k--;
  }
  cout << anss;
  return 0;
}