I used the dynamic programming approach to solve the problem, but my program 
failed at the following input for large data:

7 36

The correct output is 16 while my output is 24.

This test case could be reduced to the input of

7 12

where the correct output (by the programs from others) is 16 and my output is 
still 24.

However, when I try to check the result by hand using the following 
representation:

Block A2 (period = 1)
333333333333
333333333333

Block B3 (period = 4)
222122212221
212121212121
212221222122

Block C2 (period = 3)
221221221221
221221221221

Block D2 (period = 6)
211222211222
222211222211

Block E1 (period = 1)
222222222222

I get the following results:

Input 4 12
Output 5 (Correct)
1: A2 + C2
2: A2 + D2
3: C2 + A2
4: D2 + A2
5: E1 + A2 + E1

Input 5 12
Output 7 (Correct)
1: A2 + B3
2: A2 + E1 + A2
3: B3 + A2
4: C2 + A2 + E1
5: D2 + A2 + E1
6: E1 + A2 + C2
7: E1 + A2 + D2

Input 6 12
Output 21 (Correct)
1: A2 + C2 + A2  (p3 +)  (Note: p3 means period = 3, + means ended with A2)
2: A2 + D2 + A2  (p6 +)
3: A2 + E1 + A2 + E1  (p1)
4: B3 + A2 + E1  (p4)
5,6,7: C2 + A2 + D2 (p6)
8,9,10: C2 + A2 + C2 (p3)
11,12,13: D2 + A2 + C2 (p6)
14,15,16,17,18,19: D2 + A2 + D2 (p6)
20: E1 + A2 + B3 (p4)
21: E1 + A2 + E1 + A2 (p1 +)

Input 7 12
Output 24 (Incorrect)
1:                              A2 + B3 + A2 (p4 +)
2:                              A2 + C2 + A2 + E1 (p3)
3:                              A2 + D2 + A2 + E1 (p6)
4:                              A2 + E1 + A2 + C2 (p3)
5:                              A2 + E1 + A2 + D2 (p6)
6,7,8:                          B3 + A2 + C2 (p12)  (3 combinations)
9,10,11,12:                     B3 + A2 + D2 (p12)  (4 combinations)
13,14,15:                       C2 + A2 + B3 (p12)  (3 combinations)
16,17,18,19:            D2 + A2 + B3 (p12)  (4 combinations)
20:                             C2 + A2 + E1 + A2 (p3 +)
21:                             D2 + A2 + E1 + A2 (p6 +)
22:                             E1 + A2 + C2 + A2 (p3 +)
23:                             E1 + A2 + D2 + A2 (p6 +)
24:                             E1 + A2 + E1 + A2 + E1 (p1)

I still cannot figure out what cases among the 24 I listed are duplicated or 
wrong. Could anybody point it out for me?

Thanks in advance!

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