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;
string pre[55], back[55];
int main() {
  int n, k;
  string t, s;
  cin >> n >> k >> t;
  s = t;
  k--;
  if (n == 1) {
    k++;
    while (k--) cout << t;
    cout << endl;
    return 0;
  }
  pre[1] = t[0];
  for (int i = 2; i <= n; i++) pre[i] = pre[i - 1] + t[i - 1];
  for (int i = 1; i < s.size() && k; i++) {
    if (s.substr(i, s.size()) == pre[(s.substr(i, s.size()).size())]) {
      s = s.substr(0, i) + t;
      k--;
    } else if (i == s.size() - 1) {
      s += t;
      k--;
      i++;
    }
    if (k == 0) break;
  }
  cout << s << endl;
  return 0;
}