The Knight's Tour

Problem Background

Special for beginners, ^_^

Problem Description

In Chinese chess, the knight moves in an "L" shape (日字形).

Write a program that, given an $n\times m$ board and the knight's starting position $(x,y)$, computes how many paths allow the knight to traverse every point on the board without revisiting the same point.

Input Format

The first line is an integer $T\;(T < 10)$, the number of test cases.

Each test case contains one line of four integers: the board size and the starting coordinates $n, m, x, y\;(0\le x\le n-1,\;0\le y\le m-1,\;m\le 5,\;n\le 5)$.

Output Format

For each test case, output one line with one integer: the total number of paths by which the knight can traverse the board; $0$ means it cannot be traversed.

Sample Input

1
5 4 0 0

Sample Output

32

Constraints

1s, 1024KiB for each test case.