There is a box protected by a password. The password is n digits, where each letter can be one of the first k digits 0, 1, …, k-1.

You can keep inputting the password, the password will automatically be matched against the last n digits entered.

For example, assuming the password is “345”, I can open it when I type “012345”, but I enter a total of 6 digits.

Please return any string of minimum length that is guaranteed to open the box after the entire string is inputted.

Example 1:

Input: n = 1, k = 2
Output: "01"
Note: "10" will be accepted too.

Example 2:

Input: n = 2, k = 2
Output: "00110"
Note: "01100", "10011", "11001"

Note:
n will be in the range [1, 4].
k will be in the range [1, 10].
k^n will be at most 4096.

class Solution {
    public String crackSafe(int n, int k) {
        int M = (int) Math.pow(k, n-1);
        int[] P = new int[M * k];
        for (int i = 0; i < k; ++i)
            for (int q = 0; q < M; ++q)
                P[i*M + q] = q*k + i;

        StringBuilder ans = new StringBuilder();
        for (int i = 0; i < M*k; ++i) {
            int j = i;
            while (P[j] >= 0) {
                ans.append(String.valueOf(j / M));
                int v = P[j];
                P[j] = -1;
                j = v;
            }
        }

        for (int i = 0; i < n-1; ++i)
            ans.append("0");
        return new String(ans);
    }
}