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() {
  int a, b;
  string s;
  cin >> a >> b >> s;
  bool flag = false;
  int i = 0, k = 0;
  for (i = 0; i < a; ++i) {
    if (!flag) {
      if (s.substr(i, a) == s.substr(0, a - i) && i != 0) {
        flag = true;
      } else
        k++;
    } else
      break;
  }
  string w = "";
  if (!flag)
    for (int j = 0; j < b; j++) {
      w += s;
    }
  else {
    w = s;
    for (int j = 0; j < b - 1; j++) {
      w += s.substr(a - k, a);
    }
  }
  cout << w << endl;
  return 0;
}