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 n, k, last;
string s, res;
void cek() {
  for (int i = last + 1; i < res.size(); i++) {
    int cur = 0;
    bool temp = false;
    for (int j = i; j < res.size() and cur < s.size(); j++) {
      if (s[cur] != res[j]) {
        temp = true;
        break;
      }
      cur++;
    }
    if (!temp) {
      last = i;
      for (int j = cur; j < s.size(); j++) {
        res += s[j];
      }
      return;
    }
  }
  last = res.size();
  for (int j = 0; j < s.size(); j++) {
    res += s[j];
  }
  return;
}
int main() {
  scanf("%d %d", &n, &k);
  cin >> s;
  res += s;
  last = 0;
  k--;
  while (k--) {
    cek();
  }
  cout << res << endl;
}