Placing Two Snakes

Two snakes, Kiki and Susu, like to play on an $n \times m$ rectangular grid. Once the game is under way they ignore the rules and mix themselves up, but the arrangement they start the game from follows these rules.

1. Each snake is one rectangle whose shorter side has length 1. Kiki covers $k$ cells and Susu covers $s$ cells.
2. Each snake lies either horizontally or vertically.
3. Both snakes fit completely inside the grid.
4. No cell is covered by both snakes.

In the picture below, the top two arrangements are valid and the bottom two are invalid. The grid is $5 \times 5$ and both snakes have length 3.

Which end holds the head is part of the arrangement. An arrangement with the head at $(x_1, y_1)$ and the tail at $(x_2, y_2)$ is different from the one with the head at $(x_2, y_2)$ and the tail at $(x_1, y_1)$. A snake of length 1 has its head and tail on the same cell, so it has no direction to tell apart and only the cell it sits on distinguishes it. Kiki and Susu are different snakes, so exchanging their two positions also gives a different arrangement.

Given the grid size $n$, $m$ and the lengths $k$ of Kiki and $s$ of Susu, count the arrangements the game can start from.

The first line contains the number of test cases $T$. ($1 \le T \le 100\,000$)

Each of the next $T$ lines holds one test case: the grid size $n$, $m$ and the lengths $k$ of Kiki and $s$ of Susu, separated by spaces. ($1 \le n, m \le 100\,000$, $1 \le k, s \le \min(n, m)$)

For each test case print one line in the form Case c: x. Here $c$ is the test case number starting from 1, and $x$ is the number of arrangements modulo $1\,000\,000\,007$ ($= 10^9 + 7$).