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;
int32_t main() {
  long long int n, k;
  cin >> n >> k;
  string str;
  cin >> str;
  long long int maxl = 0;
  long long int j;
  for (j = n - 1; j >= 1; j--) {
    long long int ptr1 = 0;
    long long int ptr2 = j;
    bool result = true;
    long long int count = 0;
    while (ptr1 < n && ptr2 < n) {
      if (str[ptr1] != str[ptr2]) {
        result = false;
        break;
      } else {
        count++;
      }
      ptr1++;
      ptr2++;
    }
    if (result) maxl = max(maxl, count);
  }
  cout << str;
  for (j = 0; j < k - 1; j++) {
    for (long long int i = maxl; i < n; i++) {
      cout << str[i];
    }
  }
  cout << '\n';
}