Today on a math lesson the teacher told Vovochka that the Euler function of a positive integer φ(n) is an arithmetic function that counts the positive integers less than or equal to n that are relatively prime to n. The number 1 is coprime to all the positive integers and φ(1) = 1. Now the teacher gave Vovochka an array of n positive integers a1, a2, ..., an and a task to process q queries li ri -- to calculate and print modulo 109 + 7. As it is too hard for a second grade school student, you've decided to help Vovochka. The first line of the input contains number n (1 ≤ n ≤ 200 000) -- the length of the array given to Vovochka. The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 106). The third line contains integer q (1 ≤ q ≤ 200 000) -- the number of queries. Next q lines contain the queries, one per line. Each query is defined by the boundaries of the segment li and ri (1 ≤ li ≤ ri ≤ n). Print q numbers -- the value of the Euler function for each query, calculated modulo 109 + 7. In the second sample the values are calculated like that: