Home

Problem Statement

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:

• $a_x + a_{x+1} + ... + a_{y-1} = X$
• $a_y + a_{y+1} + ... + a_{z-1} = Y$
• $a_z + a_{z+1} + ... + a_{w-1} = Z$

Since the answer can be extremely large, print the number modulo $10^9+7$.

Constraints

• $3 ≦ N ≦ 40$
• $1 ≦ X ≦ 5$
• $1 ≦ Y ≦ 7$
• $1 ≦ Z ≦ 5$

Sample Input 1

3 5 7 5

Sample Output 1

1

Here, the only sequence that contains a $5,7,5$-Haiku is $[5, 7, 5]$.

Sample Input 2

4 5 7 5

Sample Output 2

34

Sample Input 3

37 4 2 3

Sample Output 3

863912418

Sample Input 4

40 5 7 5

Sample Output 4

562805100