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() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long int n, k;
  cin >> n >> k;
  string s;
  cin >> s;
  string hero;
  long long int subsize = INT_MIN;
  for (int i = 1; i < s.length(); i++) {
    long long int inc = 0, flag = 0;
    for (int j = 0; j < s.length() - i; j++) {
      if (s[i + inc] == s[j]) flag++;
      if (s[i + inc] != s[j]) break;
      if (i + inc == s.length() - 1) {
        subsize = max(subsize, flag);
        flag = 0;
      }
      inc++;
    }
  }
  if (subsize < 0) subsize = 0;
  for (int i = subsize; i < s.length(); i++) hero += s[i];
  k--;
  while (k--) s += hero;
  cout << s;
  return 0;
}