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;
const int mod = 1000000007;
const int inf = 2012345678;
const int N = 2e5 + 10;
string s, ans, tmp;
bool ch() {
  int i = 0;
  while (s[i] == tmp[i] && i < tmp.length()) ++i;
  return i == tmp.length();
}
int main() {
  int n, k;
  cin >> n >> k >> s;
  ans = s, --k;
  int ps = 1;
  while (k--) {
    while (true) {
      if (ps == ans.length()) {
        ans += s, ps = ans.length();
        break;
      }
      tmp = ans.substr(ps);
      if (ch()) {
        for (int i = tmp.length(); i < (int)(s.length()); ++i) ans += s[i];
        ++ps;
        break;
      } else
        ++ps;
    }
  }
  cout << ans << endl;
}