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 maxn = 4e5 + 5;
int main() {
  int n, k;
  while (~scanf("%d %d", &n, &k)) {
    string a;
    cin >> a;
    string tmp;
    bool flag = 0;
    for (int i = n - 1; i >= 0; i--) {
      if (a.substr(0, i) == a.substr(n - i)) {
        tmp = a.substr(i);
        flag = 1;
        break;
      }
    }
    if (flag == 0) {
      tmp = a;
    }
    cout << a;
    for (int i = 1; i < k; i++) {
      cout << tmp;
    }
    cout << endl;
  }
}