Score : 600 points
Snuke, a water strider, lives in a rectangular pond that can be seen as a grid with H east-west rows and W north-south columns. Let (i,j) be the square at the i-th row from the north and j-th column from the west.
Some of the squares have a lotus leaf on it and cannot be entered.
The square (i,j) has a lotus leaf on it if c_{ij} is @
, and it does not if c_{ij} is .
.
In one stroke, Snuke can move between 1 and K squares (inclusive) toward one of the four directions: north, east, south, and west. The move may not pass through a square with a lotus leaf. Moving to such a square or out of the pond is also forbidden.
Find the minimum number of strokes Snuke takes to travel from the square (x_1,y_1) to (x_2,y_2). If the travel from (x_1,y_1) to (x_2,y_2) is impossible, point out that fact.
.
or @
..
.
Input is given from Standard Input in the following format:
H W K x_1 y_1 x_2 y_2 c_{1,1}c_{1,2} .. c_{1,W} c_{2,1}c_{2,2} .. c_{2,W} : c_{H,1}c_{H,2} .. c_{H,W}
Print the minimum number of strokes Snuke takes to travel from the square (x_1,y_1) to (x_2,y_2), or print -1
if the travel is impossible.
3 5 2 3 2 3 4 ..... .@..@ ..@..
5
Initially, Snuke is at the square (3,2). He can reach the square (3, 4) by making five strokes as follows:
From (3, 2), go west one square to (3, 1).
From (3, 1), go north two squares to (1, 1).
From (1, 1), go east two squares to (1, 3).
From (1, 3), go east one square to (1, 4).
From (1, 4), go south two squares to (3, 4).
1 6 4 1 1 1 6 ......
2
3 3 1 2 1 2 3 .@. .@. .@.
-1