REQ

3000ms

262144K

Description:

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, ..., a_n and a task to process q queries l_i r_i — to calculate and print $\text{[math]}$ 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, ..., a_n (1 ≤ a_i ≤ 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 l_i and r_i (1 ≤ l_i ≤ r_i ≤ n).

Output:

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

Sample Input:

10
1 2 3 4 5 6 7 8 9 10
7
1 1
3 8
5 6
4 8
8 10
7 9
7 10

Sample Output:

Sample Input:

7
24 63 13 52 6 10 1
6
3 5
4 7
1 7
2 4
3 6
2 6

Sample Output:

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

Informação

Provedor Codeforces

Código CF594D