Given an integer `x`

an array of n elements `[a1,a2,a3 ... an]`

(both of which will be taken from input stream) , we wish to find out `(x % a1) + (x % a2) + (x % a3) ... + (x % an)`

. `x`

will be given after the taking array as the input.

Since this is part of a bigger problem, I want to find it out preferably in `O(1)`

time (excluding `O(n)`

time for taking in the array).

When I will take the input array, I will simultaneously calculate the sum of the complete array, and wish to bring it into a format similar to `(x % (a1 + a2 + a3 ... an))`

. Is there any identity similar to this?

This is not my actual problem. I just wish to meet my time complexity requirements. Once the array is taken as input, after that, `multiple numbers`

will be given … and I have to calculate the answer for each of them in O(1) time.

Source: Windows Questions C++