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;
char s[55];
int main() {
  int x, a;
  cin >> x >> a;
  cin >> s + 1;
  int len = 0;
  for (int i = 1; i < x; i++) {
    int flag = 0;
    int j;
    for (j = 1; j <= i; j++) {
      if (s[j] != s[x - i + j]) {
        flag = 1;
      }
    }
    if (flag == 0) len = j - 1;
  }
  for (int i = 1; i <= a - 1; i++) {
    for (int j = 1; j <= x - len; j++) {
      cout << s[j];
    }
  }
  cout << s + 1 << endl;
  return 0;
}