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;
int p[55];
string t;
void getp() {
  int j = 0;
  p[0] = p[1] = 0;
  for (int i = 1; i < t.length(); ++i) {
    while (j && t[j] != t[i]) j = p[j];
    if (t[j] == t[i]) j++;
    p[i + 1] = j;
  }
}
void build() {
  getp();
  string ans = t;
  int cnt = 1;
  while (cnt < k) {
    for (int i = p[t.length()]; i < t.length(); ++i) ans.append(1, t[i]);
    cnt++;
  }
  cout << ans;
}
int main() {
  cin >> n >> k >> t;
  build();
  return 0;
}