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Problem 5138. -- [Usaco2017 Dec]Push a Box

5138: [Usaco2017 Dec]Push a Box

Time Limit: 10 Sec  Memory Limit: 512 MB
Submit: 145  Solved: 31
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Description

Bessie and her friends have invented a new game. The game is named accurately, but not particularly 
creatively. They call it the "Push A Box Around The Barn To Get It In The Right Spot And Don't Move 
The Hay" game (if you think that's excessive, you should see some of the variable names the cows use
 when they write code...)The barn can be modeled as an N×M rectangular grid. Some of the grid cells
 have hay in them. Bessie occupies one cell in this grid, and a large wooden box occupies another ce
ll. Bessie and the box are not able to fit in the same cell at the same time, and neither can fit in
to a cell containing hay.Bessie can move in the 4 orthogonal directions (north, east, south, west) a
s long as she does not walk into hay. If she attempts to walk to the space with the box, then the bo
x will be pushed one space in that direction, as long as there is an empty cell on the other side. I
f there is no empty cell, then Bessie will not be able to make that move.A certain grid cell is desi
gnated as the goal. Bessie's goal is to get the box into that location.Given the layout of the barn,
 including the starting positions of the box and the cow, and the target position of the box, determ
ine if it possible to win the game.

Input

The first line has three numbers, N, M, and Q, 
where N is the number of rows in the grid and M is the number of columns.
1≤N,M≤1500
1≤Q≤50,000
On the next N lines is a representation of the grid, 
where characters represent empty cells (.), hay (#),
Bessie's starting position (A), and the box's initial location (B).
This is followed by Q lines, each with a pair of integers (R,C). 
For each pair, you should determine if it is possible to get the box to that cell at row R, column C, 
starting from the initial state of the barn. The top row is row 1, and the left column is column 1.

Output

Q lines, each with either the string "YES" or "NO".

Sample Input

5 5 4
##.##
##.##
A.B..
##.##
##.##
3 2
3 5
1 3
5 3

Sample Output

NO
YES
NO
NO
To push the box to the position (3, 5), the cow just needs to move 3 spaces to the right.
None of the other three positions are attainable.

HINT

Source

Platinum

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