input:

3 10
^>^<^^^^>^
<v^v^^v^v>
<>vvvvvvvv
10 1
v
^
<
<
v
<
v
>
<
<
5 4
<^^^
<vvv
<<^>
vv^v
<vvv
2 9
^^^^^^^^^
vvvvvvvvv
9 10
^>^^<^<^<>
<^<<><<<<>
v^v^^<>^<^
^<vvv<><<>
<v>>><^v^>
^^^^>^^<<v
v^v>v^v^<>
v^vvv>v^<^
vvvvv><>v>
8 8
^^^^<^<^
<>^<v>v^
<v<v>^v>
v>v<vv<>
^<^>>v<>
<v^v^<<>
^v^^>v<>
<vv<vv<>
2 2
...

output:

10
0
5
6
33
23
0
5
21
15
17
0
9
2
1
11
0
9
6
0
0
1
0
10
10
13
5
9
6
17
3
0
6
10
7
4
0
8
0
35
9
2
10
2
13
4
18
11
17
0
0
17
0
4
12
12
9
23
24
5
1
19
8
6
10
12
11
1
12
0
13
11
3
25
2
21
9
0
3
0
0
23
31
12
2
15
25
21
18
12
0
1
0
20
13
7
11
0
0
26
6
3
18
12
4
25
11
19
0
8
26
1
7
0
12
33
21
11
6
0
0
4
5
...

result: