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: Flip all the lights. Flip lights with even numbers. Flip lights with odd numbers. 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].