Multiplication Madness

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Points: 7 (partial)
Time limit: 2.0s
Memory limit: 256M

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Problem type

Nugget has failed his most recent math test on multiplication. To help him improve, Bruce has given Nugget N queries about multiplication. Each query comes in the form: x y, where x and y are non-negative integers. To solve the query, you must print out the product of all the integers between x and y (inclusive) modulo 10^9 + 7. Being a very lazy busy boy, Nugget asks you to build a program that can do this for him. As a reward, he offers you 7 points.

Note: If you are using Python 2/3, you should submit using PyPy 2/3 with fast I/O

Input Specification

The first line will contain a positive integer N representing the number of queries.

The next N lines will contain non-negative integers x and y separated by a space.

Output Specification

On the i^{\text{th}} line, output the product of the integers between x and y modulo 10^9 + 7 of the i^{\text{th}} query.

Constraints

For all subtasks:

1 \le N \le 10^6

0 \le x \le y \le 10^{6}

Subtask 1 [15%]:

1 \le N \le 10

Subtask 2 [85%]:

No additional constraints.

Sample Input 1

4
1 4
2 4
3 4
4 4

Sample Output 1

24
24
12
4

Sample Input 2

3
10 999
17 1910
500000 505000

Sample Output 2

66208545
58404876
841914375

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