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() {
  int n, k;
  cin >> n >> k;
  string s, s2;
  cin >> s;
  s2 = s;
  s += " ";
  int flag = 0;
  for (int i = 1; i < n + 1; i++) {
    if (s[i] == s[0]) {
      int j = i;
      while (s[j] == s[j - i]) {
        j++;
      }
      if (j == n) {
        flag = i;
        break;
      }
    }
  }
  if (flag != 0) {
    for (int j = 0; j < k; j++) {
      for (int i = 0; i < flag; i++) {
        cout << s[i];
      }
    }
    for (int i = flag; i < n; i++) {
      cout << s[i];
    }
  } else {
    for (int i = 0; i < k; i++) {
      cout << s2;
    }
  }
  return 0;
}