Problem Statement
Limak is a big grizzly bear. He is now going to destroy an entire forest.
Limak's forest is a rectangular grid that consists of W columns by H rows of cells. At the beginning a single tree grows in each cell. The forest is aligned with the major compass directions: row numbers increase towards the South and column numbers increase towards the East.
Limak will destroy the forest by pushing some of the trees. Whenever Limak pushes a tree, the tree will fall down and remain lying both in the current cell and in the next cell in the direction in which it was pushed. For example, if Limak pushes the tree that grows in the cell (r,c) southwards, he will obtain a toppled tree that lies in the cells (r,c) and (r+1,c).
When pushing the trees, Limak always follows a few rules:
- He only pushes trees in two directions: either southwards or eastwards.
- He will never push a tree in a way that would cause it to fall out of the forest. For example, he will never push a tree in the last column eastwards.
- He will never push a tree in a way that would produce two fallen trees lying on the same cell.
There is a single letter written on each of the trees. Each of these letters is either S or E (representing South and East, respectively). When pushing a tree, Limak will prefer the direction that is written on the tree. For example, if a tree has the letter S, Limak will push it southwards if possible.
Limak is going to visit each cell in the forest exactly once, in row major order. I.e., first he will visit all the cells in the first row from left to right, then the cells in the second row from left to right, and so on. In each cell he will act according to the following algorithm:
- Is there a fallen tree in the current cell? If yes, there is no room here to do anything, so I'll just move to the next cell.
- Can I push the tree in the direction that is given by the letter written on the tree? If yes, I'll do so and move to the next cell.
- Can I push the tree in the other direction? If yes, I'll do so and move to the next cell.
- I'll move to the next cell without pushing the tree.
See Example 0 for a sample execution of Limak's algorithm.
You are given the
Definition
- Class:
- BearDestroysDiv2
- Method:
- sumUp
- Parameters:
- int, int, int
- Returns:
- int
- Method signature:
- int sumUp(int W, int H, int MOD)
- (be sure your method is public)
Constraints
- W will be between 1 and 7, inclusive.
- H will be between 1 and 40, inclusive.
- MOD will be between 3 and 10^9, inclusive.
- MOD will be prime.
Examples
4
3
999999937
Returns: 24064
There are 2^(4*3) = 2^12 = 4096 different forests with W=4 columns and H=3 rows. One of those forests looks as follows: SEEE ESSS EESS When destroying this forest, Limak will push five trees. In the scheme below, the final locations of the toppled trees are shown using the numbers 1 through 5. The trees are numbered in the order in which Limak pushed them. The two cells that do not contain a fallen tree at the end are denoted by underscores. 1223 1453 _45_ It can be shown that for these dimensions there are exactly 512 forests in which Limak would topple exactly 5 trees. In each of the remaining (4096-512) forests Limak would topple 6 trees. Thus, the return value is 512 * 5 + (4096-512) * 6.
3
4
999999937
Returns: 24576
For these dimensions of the forest Limak will always topple exactly 6 trees. The return value is 6 * 2^12.
2
20
584794877
Returns: 190795689
For these dimensions of the forest Limak will always topple exactly 20 trees. The return value is (20 * 2^40) modulo MOD.
5
10
3
Returns: 2
1
1
19
Returns: 0
7
40
312880987
Returns: 256117818
1
1
71876209
Returns: 0
1
2
483128897
Returns: 4
1
3
442951021
Returns: 8
1
4
366999047
Returns: 32
1
5
3
Returns: 1
2
1
643643149
Returns: 4
2
2
291474539
Returns: 32
2
3
633529777
Returns: 192
2
4
7
Returns: 2
2
5
108313867
Returns: 5120
3
1
975807823
Returns: 8
3
2
232315729
Returns: 192
3
3
11
Returns: 2
3
4
253520207
Returns: 24576
3
5
781548307
Returns: 229376
4
1
73185317
Returns: 32
4
2
257580319
Returns: 1024
4
3
908346931
Returns: 24064
4
4
110648963
Returns: 522240
4
5
748527467
Returns: 10354688
5
1
496986739
Returns: 64
5
2
836042177
Returns: 5120
5
3
11
Returns: 4
5
4
3
Returns: 1
5
5
13
Returns: 11
1
40
13
Returns: 8
7
1
246931759
Returns: 384
2
40
543491279
Returns: 305520570
7
2
431566237
Returns: 114688
3
40
422344259
Returns: 100200332
7
3
932041361
Returns: 20938752
4
40
653858027
Returns: 486979880
5
40
5
Returns: 2
3
33
338057281
Returns: 229234113
4
10
673227689
Returns: 300090229
1
2
519275041
Returns: 4
7
20
204635693
Returns: 113263323
7
3
291198361
Returns: 20938752
3
27
754290517
Returns: 521712476
6
12
153692323
Returns: 134236843
5
15
89654479
Returns: 52084944
7
1
759804347
Returns: 384
7
24
945707647
Returns: 224739679
7
40
476882267
Returns: 197168764
7
39
226092029
Returns: 218121254
7
38
521517259
Returns: 358484312
7
37
18861637
Returns: 2388729
7
36
5
Returns: 0
7
35
62988109
Returns: 36393817
7
34
763736669
Returns: 690035012
6
40
615400307
Returns: 467682622
6
39
863998307
Returns: 105866078
6
38
11
Returns: 9
6
37
623550203
Returns: 436670574
6
36
130471169
Returns: 39616000
6
35
747432841
Returns: 152857752
6
34
668902831
Returns: 428552389
5
40
857873893
Returns: 394867891
5
39
10639481
Returns: 10034404
5
38
121972309
Returns: 86849625
5
37
219726329
Returns: 169427842
5
36
3
Returns: 0
5
35
366586403
Returns: 354218015
5
34
226377817
Returns: 11359520
7
40
97837079
Returns: 18106495
7
40
684074123
Returns: 522878364
7
40
3
Returns: 0
7
36
312880987
Returns: 197986862
7
39
1000003
Returns: 975462