Number Puzzle

A number puzzle asks you to connect equal marked numbers on a grid with a single unbroken line. In this problem the grid has the digit $1$ written in exactly two distinct cells, and you must decide whether a line satisfying all of the following rules can be drawn.

• The line is a single unbroken path; it never branches and never crosses itself.
• The line passes through every cell of the grid exactly once.
• The two cells holding $1$ are the two endpoints of the line.

Equivalently, treat every cell as a vertex and join two cells that are adjacent up, down, left, or right. The question is whether a path that starts at one $1$, ends at the other, and visits every cell exactly once exists.

The grid has size $m \times n$, where both $m$ and $n$ are even.

The first line contains the number of test cases $T$.

Each test case consists of three lines. The first line contains the number of rows $m$ and the number of columns $n$, separated by a space ($2 \le m, n \le 100$; both $m$ and $n$ are even). The second line gives the position of the first $1$ as a row $i$ and a column $j$, and the third line gives the position of the second $1$ as a row $a$ and a column $b$ ($1 \le i, a \le m$, $1 \le j, b \le n$). The two positions are different.

For each test case, print $1$ if such a line can be drawn, or $-1$ if it cannot, on its own line.