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