There is a room with n lights which are turned on initially and 4 buttons on the wall. After performing exactly m unknown operations towards buttons, you need to return how many different kinds of status of the n lights could be.

Suppose n lights are labeled as number [1, 2, 3 ..., n], function of these 4 buttons are given below:

1. Flip all the lights.
2. Flip lights with even numbers.
3. Flip lights with odd numbers.
4. Flip lights with (3k + 1) numbers, k = 0, 1, 2, ...

Example 1:

Input: n = 1, m = 1.
Output: 2
Explanation: Status can be: [on], [off]

Example 2:

Input: n = 2, m = 1.
Output: 3
Explanation: Status can be: [on, off], [off, on], [off, off]

Example 3:

Input: n = 3, m = 1.
Output: 4
Explanation: Status can be: [off, on, off], [on, off, on], [off, off, off], [off, on, on].

Note:n and m both fit in range [0, 1000].

class Solution:
    def flipLights(self, n, m):
        """
        :type n: int
        :type m: int
        :rtype: int
        """
        n 
 
= min(n, 3)
        if m == 0: return 1
        if m == 1: return [2, 3, 4][n-1]
        if m == 2: return [2, 4, 7][n-1]
        return [2, 4, 8][n-1]

672. Bulb Switcher II 燈泡切換器II