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;
  string str;
  cin >> n >> k >> str;
  int sub = 0, cnt = 1;
  for (int i = 1; i < n; i++)
    if (str[i - 1] == str[i]) cnt++;
  if (cnt == n) {
    string ans = str;
    for (int i = 1; i < k; i++) ans += str[0];
    cout << ans;
    return 0;
  }
  for (int i = 1; i <= n; i++) {
    string s1 = str.substr(0, i);
    string s2 = str.substr(n - i);
    if (s1 == s2 && i != n) {
      sub = i;
    }
  }
  string s = str.substr(sub);
  string ans = str;
  for (int i = 1; i < k; i++) ans += s;
  cout << ans;
  return 0;
}