## 15 Jan Aurora Wednesday 18:30 Python Practice 23.01.11.

**Question:**

Once upon an ancient time, a knight was preparing for the great battle in GridLand. The GridLand is divided into square grids. There are *R* horizontal and *C* vertical grids. Our particular knight in this case can always give an (*M*, *N*) move, i.e. he can move *M* squares horizontally and *N* squares vertically or he can move *M* squares vertically and *N* squares horizontally in a single move. In other words he can jump from square (*a*, *b*) to square (*c*, *d*) if and only if, either (|*a*−*c*| = *M* and |*b*−*d*| = *N*) or (|*a* − *c*| = *N* and |*b* − *d*| = *M*). However, some of the squares in the war field are filled with water. For a successful jump from one square to another, none of the squares should contain water. Now, the knight wants to have a tour in the war field to check if everything is alright or not. He will do the following:

- He will start and end his tour in square (0, 0) but visit as many squares as he can.
- For each square s
, he counts the number_{i}*k*of distinct squares, from which he can reach s_{i}in one jump (satisfying the jumping condition). Then he marks the square as an even square if_{i}*k*is even or marks it odd if_{i}*k*is odd. The squares he cannot visit remain unmarked._{i} - After coming back to square (0, 0) he counts the number of even and odd marked squares. He can visit a square more than once.

You, as an advisor of the knight, suggested that, he can do it without visiting all the squares, just by writing a program. So the knight told you to do so. He will check your result at the end of his visit.

**Input**

The first line of input will contain *T* (≤ 50) denoting the number of cases. Each case starts with four integers *R*, *C*, *M*, *N* (1 < *R*, *C* ≤ 100, 0 ≤ *M*, *N* ≤ 50, *M* + *N* > 0). Next line contains an integer *W* (0 ≤ *W* < *R* ∗ *C*), which is the number of distinct grids containing water. Each of the next *W* lines contains a pair of integer *x _{i}* ,

*y*(0 ≤

_{i}*x*<

_{i}*R*, 0 ≤

*y*<

_{i}*C*,

*x*+

_{i}*y*> 0).

_{i}**Output**

For each case, print the case number and the number of even and odd marked squares.

Sample Input2 3 3 2 1 0 4 4 1 2 2 3 3 1 1Sample OutputCase 1: 8 0 Case 2: 4 10

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