I was trying to solve this problem

let, int **moded** = x % A here, the highest value of **moded** can be A-1;

but if we add some other numbers.. then.. (x % A1) + (x % A2) + .... + (x % An) then what can be the highest result if we add all the **moded** from Ai to An for this sequence?

for each Ai, if we take Ai-1, then the result will be maximum, but will there always exist an x if we were to get this maximum result?

There always exists such $$$m$$$.

Copy pasting from editorial.

Let $$$m=a_1*a_2...a_n$$$

Then $$$m-1$$$ is the required $$$x$$$.

Thank you. From what you said, I figured maybe x = lcm(a1, a2, ..., aN) — 1

but how x = (a1∗a2...aN) — 1 ?

it can be any multiple of LCM.

let say [3 4 6]

you will get same remainder from X=lcm(3,4,6)-1 or X=3*4*6-1

okay, Thank you!