Score : 700 points
Haiku is a short form of Japanese poetry. A Haiku consists of three phrases with 5, 7 and 5 syllables, in this order.
Iroha is looking for X,Y,Z-Haiku (defined below) in integer sequences.
Consider all integer sequences of length N whose elements are between 1 and 10, inclusive. Out of those 10^N sequences, how many contain an X,Y,Z-Haiku?
Here, an integer sequence a_0, a_1, ..., a_{N-1} is said to contain an X,Y,Z-Haiku if and only if there exist four indices x, y, z, w (0 ≦ x < y < z < w ≦ N) such that all of the following are satisfied:
Since the answer can be extremely large, print the number modulo 10^9+7.
The input is given from Standard Input in the following format:
N X Y Z
Print the number of the sequences that contain an X,Y,Z-Haiku, modulo 10^9+7.
3 5 7 5
1
Here, the only sequence that contains a 5,7,5-Haiku is [5, 7, 5].
4 5 7 5
34
37 4 2 3
863912418
40 5 7 5
562805100