If the query be like *“Find the number of distinct prime factors of the product of all elements of the sub array”*

For example if the array be like [2 4 3 15 16] (zero based indexing)

then the query on (0 to 2) should return answer as 2.

Because distinct prime factors of 2,4,3 are 2 & 3.

Can anyone please suggest a efficient solution to this assuming size of array be n<10^5

& number of queries q <=2^n ?

Time limit be 1 seconds .