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 READ(string INPUT = "NO", string OUTPUT = "NO") {
  if (INPUT != "NO") freopen(INPUT.c_str(), "r", stdin);
  if (OUTPUT != "NO") freopen(OUTPUT.c_str(), "w", stdout);
}
map<string, bool> Prefix;
map<string, string> rest;
int main() {
  int n, k;
  cin >> n >> k;
  string x, ans;
  cin >> x;
  ans = x;
  for (int i = 1; i <= n; i++) {
    Prefix[x.substr(0, i)] = 1;
    rest[x.substr(0, i)] = x.substr(i);
  }
  k--;
  int st = 1;
  while (k--) {
    if (st >= (int)ans.size()) {
      ans += x;
      st++;
      continue;
    }
    for (int i = st; i < (int)ans.size(); i++) {
      if (Prefix[ans.substr(i, (int)ans.size() - i)]) {
        ans += rest[ans.substr(i, (int)ans.size() - i)];
        st = i + 1;
        break;
      }
      if (i + 1 == (int)ans.size()) ans += x;
    }
  }
  cout << ans << "\n";
  return 0;
}