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(void) {
  int n, k;
  char c[55];
  cin >> n >> k >> c;
  int cnt = 0;
  for (int i = 0; i < n - 1; i++) {
    int same = 0;
    if (c[i] == c[n - 1]) {
      int ok = 1;
      for (int j = i - 1; j >= 0; j--) {
        if (c[j] != c[j + n - 1 - i]) {
          ok = 0;
          break;
        }
      }
      if (ok) same = i + 1;
    }
    cnt = max(cnt, same);
  }
  for (int i = 0; i < n; i++) cout << c[i];
  for (int j = 1; j < k; j++)
    for (int i = cnt; i < n; i++) cout << c[i];
  cout << endl;
}