Hint to this question

Pigeonhole principle: It will always be possible and the answer will always be a continuous sequence.

How to solve:

Consider N = 7:

1 2 50 3 4 0 0

The sum of the segment 1, 2, 50 is 53 and that of 1,2,50,3,4 is 60

53 % 7 = 4

60 % 7 = 4

if a % x = 1

and b % x =1

then (a-b)%x is always 0

So the segment between those two prefix sums will give 0 as modulo which is (3,4) = 7