Vishal and Priyanka are friends. Priyanka has been given a task by her teacher. Since Vishal likes Priyanka, help him in impressing her.

The task is that there are $N x M$ dots in a screen pattern lock. There are some rules for all the possible lock patterns. The lock pattern starts at the coordinates: $(X_1, Y_1)$ and ends at $(X_2, Y_2)$. From any dot, the pattern can only move in these directions: right, left or bottom. Also, the pattern never repeats over same dot.

Given $(X_1, Y_1)$ and $(X_2, Y_2)$, find out how many different patterns can exist. Since answer may be very large, output your answer modulo $(10^9+7)$.

Input Format:
The first line has an integer T which represents number of test cases.
Each test case has two lines. The first line of test case has two integers $N, M$.
The second line has four integers $X_1, Y_1, X_2, Y_2$.

Output Format:
Print answer for each test case modulo $(10^9+7)$.

Input Constraints:
$1 \le T \le 1000000$
$1 \le N,M \le 10^8$
$1 \le X_1, Y_1, X_2, Y_2 \le 10^8$

Note:
$(X_1, Y_1)$ != $(X_2, Y_2)$
$X_2 \ge X_1$