Problem:
Score : 700 points

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

Input

The input is given from Standard Input in the following format:

N X Y Z

Output

Print the number of the sequences that contain an X,Y,Z-Haiku, modulo 10^9+7.

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

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;

public class Main {
	static final long MOD = 1000000007;

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int X = sc.nextInt();
		int Y = sc.nextInt();
		int Z = sc.nextInt();
		
		int L = X+Y+Z;
		int match = 1<<(X+Y+Z-1) | 1<<(Y+Z-1) | 1<<(Z-1);
		int mask = (1<<(L-1))-1;
		
		long[][] dp = new long[N+1][1<<(L-1)];
		dp[0][0] = 1;
		for(int i=0; i<N; i++) {
			for(int j=0; j<=mask; j++) {
				for(int k=1; k<=10; k++) {
					int next = j<<k | 1<<(k-1);
					if(((next&((1<<L)-1))&match)!=match) {
						dp[i+1][next&mask] = (dp[i+1][next&mask] + dp[i][j])%MOD;
					}
				}
			}
		}
		
		long ans = 1;
		for(int i=0; i<N; i++)
			ans = (ans * 10)%MOD;
		for(int i=0; i<1<<(L-1); i++)
			ans = (ans + MOD - dp[N][i])%MOD;
		
		System.out.println(ans);
		sc.close();
	}
	
}