Can someone tell me how to solve this ?

We have an array of n elements where 1<=n<=10^5 and 1<=A[i]<=10^9 …

F(i) is ith fibonacci number

There will be q queries 1<=q<=10^5 Query is defined as:- 2 numbers l and r where 1<=l,r<=n

We have to find GCD( F(A[l]) , F(A[l+1]) … F(A[r]) )%10^9+7 where GCD of range of numbers is Greatest Common Divisor of all numbers