It seems that there are many states resulted from different operation sequences, however, if we look at operation sequences more closely(denoted 1,2,3,4 for each operation, 0 for "no change"):

When m = 1:

1=1,2=2,3=3,4=4

When m = 2:

11=0,12=3,13=2,14=14

21=3,22=0,23=1,24=24

31=2,32=1,33=0,34=34

41=14,42=24,43=34,44=0

so actually, when m = 2:

0,1,2,3,4,14,24,34

When m >=3:

I try out when m=3, the sequences are also 0,1,2,3,4,14,24,34, after cancelling the same operations(like 12=3 etc). I then made a guess when m > 3 the case would be the same.

And also list out some corner cases when n < 3 and m < 3, we get:

```
class Solution {
public:
// 1,2,3,4,11=22=33=44,14,24,34
int flipLights(int n, int m)
{
if (!m) return 1;
if (n == 1) return 2;
if (n == 2 && m == 1) return 3;
if (n == 2 && m >= 2) return 4;
if (m == 1) return 4;
if (m == 2) return 7;
return 8;
}
};
```