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 longest(string str, int n) {
  int f[n];
  f[0] = 0;
  int i = 1;
  int j = 0;
  while (i < n) {
    if (str[i] == str[j]) {
      f[i] = j + 1;
      j++;
      i++;
    } else {
      if (j > 0) {
        j = f[j - 1];
      } else {
        f[i] = 0;
        i++;
      }
    }
  }
  return f[n - 1];
}
int main() {
  int n, k;
  cin >> n >> k;
  string str;
  cin >> str;
  int l = longest(str, n);
  string str2;
  for (int i = l; i < n; i++) {
    str2 = str2 + str[i];
  }
  cout << str;
  for (int i = 1; i < k; i++) {
    cout << str2;
  }
  return 0;
}