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 n, k, l, j;
  string str, s = "";
  cin >> n >> k >> str;
  l = str.length() - 1;
  j = 1;
  while (l > 0) {
    string s1 = str.substr(0, l);
    string s2 = str.substr(j, l);
    if (s1 == s2) {
      s = str.substr(l, str.length() - l);
      break;
    }
    l--;
    j++;
  }
  if (!s.length()) s = str;
  k--;
  while (k--) {
    str = str + s;
  }
  cout << str << endl;
}