Big Table
As you can see from the name of this challenge, we are about to deal with big tables; really big tables.
There is a table of size ; rows and columns.
A sub-rectangle of the table is blocked.
We are only able to move right or down. What is the number of paths from the upper-left cell to the lower-right cell while not passing the blocked sub-rectangle?
Input Format
The first line contains an integer, , the number of test cases.
This is followed by blocks of input.
The first line of each test case contains two integers, and separated by a single space, the number of rows and columns, respectively.
The second line of each test case contains four integers, , , , and , the upper-left cell and the lower-right cell of the blocked rectangle.
Constraints
Output Format
For each test case print a line containing the answer to the corresponding test case. Print your answers modulo (109+7).
Sample Input
4
8 12
5 5 8 12
8 12
5 5 8 8
8 12
5 5 5 5
3 4
1 2 2 2
Sample Output
0
7008
23424
1