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;
const int N = 1e6 + 5, OO = 0x3f3f3f3f;
int main() {
  int n, m, i, j;
  bool e = 0;
  string s, x = "";
  cin >> n >> m >> s;
  for (int z = 1; z < s.size(); z++) {
    j = z;
    i = 0;
    while (s[j] == s[i]) {
      j++;
      i++;
      if (j == s.size()) {
        for (; i < s.size(); i++) x += s[i];
        e = 1;
        break;
      }
    }
    if (e) break;
  }
  if (!e) {
    x = s;
  }
  for (int y = 1; y < m; y++) s += x;
  cout << s << endl;
  return 0;
}