OJ Board

to solve this problem i derived the following equation for a single light bulb:
Let p is the probability of selecting the light.
So the expectation for the light will be sum over i(1 to k) : p^i * (1-p)^(k-i). Now we only need to add the terms where i is odd as only then the light will be ON.
calculating this for all the bulb is obviously time out
is there any close form? i can't find it

thanks in advance.

You can solve each test case in O(N * M * P)

I got the idea of the closed form. thanks to Jacob from codeforces

thanks anyways.