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() {
  string str, t, temp;
  int n, k, lcp[100];
  cin >> n >> k;
  cin >> str;
  lcp[0] = 0;
  for (int i = 1; i < n; i++) {
    int j = lcp[i - 1];
    while (j > 0 && (str[j] != str[i])) j = lcp[j - 1];
    if (str[i] == str[j]) j++;
    lcp[i] = j;
  }
  temp = str.substr(lcp[n - 1], n - lcp[n - 1]);
  t = str;
  for (int i = 1; i < k; i++) {
    t = t + temp;
  }
  cout << t;
}