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 gen(string ss) {
  string ss2 = ss;
  int ln = 0;
  for (int i = 0; i < ss.size() - 1; i++) {
    string pr = ss.substr(0, i + 1);
    string suff = ss.substr(ss.size() - (i + 1), i + 1);
    if (pr == suff) {
      ln = max(ln, i + 1);
    }
  }
  return ln - 1;
}
int main() {
  int n, k;
  string str;
  cin >> n >> k;
  cin >> str;
  int id = gen(str);
  if (id == -1) {
    while (k--) {
      cout << str;
    }
    return 0;
  }
  string aw = str.substr(id + 1, n - (id + 1));
  cout << str;
  k--;
  while (k--) {
    cout << aw;
  }
  return 0;
}