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>
const long long int mod = 1e9 + 7;
using namespace std;
void myfun() {
  long long int n, i, k;
  cin >> n >> k;
  string s, ss, ans;
  cin >> s;
  for (i = 1; i < n; i++) {
    long long int cn = 0, mila = 1;
    for (long long int j = i; j < n; j++) {
      if (s[j] == s[cn])
        cn++;
      else {
        mila = 0;
        break;
      }
    }
    if (mila) {
      for (long long int j = cn; j < n; j++) ss.push_back(s[j]);
      break;
    }
  }
  if (ss.size() == 0) ss = s;
  ans = s;
  k--;
  while (k > 0) {
    ans = ans + ss;
    k--;
  }
  cout << ans << "\n";
}
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  ;
  long long int t = 1;
  while (t--) myfun();
  return 0;
}