Blade Master

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Loda and Maelk are legendary ChefCraft players. They have played so many games that this number doesn't fit in
a standard 32bit integer type. Today Loda and Maelk are going to sort the things out and find out who is the
greatest ChefCraft player ever. So the great fight is coming. There are a lot of different heroes you may
choose to play ChefCraft. Obviously every hero has his pros and cons. Loda perfectly plays Blade Master. His
main skill is to make mirror images of himself to spoof the enemy.
As every other popular game ChefCraft is played on a rectangular grid which consists of N rows and
M columns. Rows of the grid are numbered by integers from 1 to N. So the upper row of the
grid has number 1 and the lower row has number N. The same holds for columns. They are numbered
by integers from 1 to M such that the most left column has number 1 while the most right
column has number M.
At the beginning of the game the only Blade Master's image stands on some starting cell (Sx, Sy) where
1 ≤ Sx ≤ N and 1 ≤ Sy ≤ M. Then Loda makes T moves. Maelk knows how the
distribution of images on the grid changes after each Loda's move. This happens according to the following
rules.
1. If there is an image standing on the cell (i, j) then the new images appear by the next
rules:
 Let F(i, j) be the total number of images in the "cross" of the cell (i, j). The "cross" of
the cell (i, j) is union of all cells in the ith row of the grid and in the jth column
of the grid. So N + M − 1 cells belongs to the "cross".
 Let X = F(i, j) mod 6, that is X is the remainder of the division of F(i, j) by
6.
 For every possible value of X we have following values: D1, D2, P1 and
P2.
 D1 and D2 may be equal to one of the 4 values ['U', 'R', 'D', 'L'] and mean
some two directions. Here 'U' means up, 'R' means right, 'D' means
down and 'L' means left.
 P1 and P2 are integer numbers.
 New mirror images will appear at every cell in the direction D1 with the period P1 starting
from cell (i, j) and in the direction D2 with the period P2 also starting from the cell
(i, j). Of course, no images will appear out of the grid. For example, if D1 = 'U' and P1 =
2 then images appear at the cells (i − 2, j), (i − 4, j), (i − 6, j), and so
on.
 Loda always use the same values for D1 and D2. Namely,
D1 = 'U', D2 = 'D' for X = 0,
D1 = 'L', D2 = 'R' for X = 1,
D1 = 'U', D2 = 'R' for X = 2,
D1 = 'R', D2 = 'D' for X = 3,
D1 = 'D', D2 = 'L' for X = 4,
D1 = 'L', D2 = 'U' for X = 5.  But values P1 and P2 may vary for different games. But once chosen they will be the same for
all moves.
2. Appearing of new mirror images happens immediately.
3. Whenever there is more than one image at the cell they start one on one fights. In each fight two
images participate and both die. So if the number of images in the cell was even than all images will
disappear in the end, otherwise exactly one image will remain at this cell.
Now Maelk wants to choose his hero in order to win the fight. The most important thing he needs to know for
this is how the number of images changes during Loda's moves. So he asks you for help. Denote by C(t)
the number of images on the grid after the tth Loda's move for t from 1 to T. For
convenience we denote C(0) = 1 with meaning that 0th move is the putting of the only Blade
Master's image at the starting cell. Maelk wants you to calculate the sum C(0) + C(1) + ... + C(T).
Since Maelk doesn't know what to expect from Loda he would like to know the answer for several values of
T. As you remember the total number of games played by Maelk and Loda at ChefCraft doesn't fit in a
standard 32bit integer type. Of course, the same can hold for the number of moves in their final fight. Since
Maelk plays ChefCraft the whole life he is not strong in math and can't calculate such large sums. So let's
help him to win the final fight and become the only ChefCraft master ever.
Input
The first line of the input contains three space separated integers N, M and Q. Here
N and M are sizes of the grid described above and Q is the number of Maelk's queries. The
second line contains two space separated integers Sx and Sy, row index and column index of the
starting position of the first image. Each of the following six lines contains two space separated integers,
the values P1 and P2 for the corresponding X, that is, ith line among these six
lines contains values P1 and P2 for X = i − 1. Each of the following Q
lines contains a single integer T, the number of Loda's moves for the corresponding Maelk's query.
Output
For every Maelk's query output on a separate line the numbers of images Maelk will see during Loda's move.
Constrains
N and M are positive
N • M ≤ 34
1 ≤ Sx ≤ N
1 ≤ Sy ≤ M
1 ≤ P1, P2 ≤ max{N, M}
1 ≤ Q ≤ 100
1 ≤ T ≤ 10^{16}
Example
Input: 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 3 Output: 4 12 17
Explanation
The initial grid looks as follows:
100
000
000
Here '1' represents a cell with an image and '0' represents a free cell.
After the first move grid is
111
000
000
After the second move grid is
101
111
111
Finally, after the third move we have
011
101
010
So after the first move Maelk will see 3 images, after the second move – 8 images and
after the third move – 5 images. Hence the answers for T = 1, 2, 3 are 1 + 3 = 4,
1 + 3 + 8 = 12 and 1 + 3 + 8 + 5 = 17 respectively.
Author:  rubanenko 
Tester:  anton_lunyov 
Editorial  http://discuss.codechef.com/problems/BMASTER 
Tags  Rubanenko, medium, oct12 
Date Added:  5082012 
Time Limit:  0.64879 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP14, JAVA, PYTH, PYTH 3.6, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, SCALA, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, PERL6, TEXT, PYP3, CLOJ, FS 
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