Please subscribe to the official Codeforces channel in Telegram via the link: https://t.me/codeforces_official. ×

D. REQ
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

Input

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).

Output

Print q numbers — the value of the Euler function for each query, calculated modulo 109 + 7.

Examples
Input
101 2 3 4 5 6 7 8 9 1071 13 85 64 88 107 97 10
Output
14608815361921441152
Input
724 63 13 52 6 10 163 54 71 72 43 62 6
Output
124876812939264112329984539136
Note

In the second sample the values are calculated like that:

• φ(13·52·6) = φ(4056) = 1248
• φ(52·6·10·1) = φ(3120) = 768
• φ(24·63·13·52·6·10·1) = φ(61326720) = 12939264
• φ(63·13·52) = φ(42588) = 11232
• φ(13·52·6·10) = φ(40560) = 9984
• φ(63·13·52·6·10) = φ(2555280) = 539136