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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

// luogu-judger-enable-o2
#include <bits/stdc++.h>
using namespace std;
long long st;
long long n,x,y,z;
int state;
const long long si=1e9+7;
long long dp[45][1<<17];
int main()
{
	scanf("%d%d%d%d",&n,&x,&y,&z);
	long long ans=1;
	for (int i=1;i<=n;i++)
	ans=(ans*10)%si;
	st=(1<<z-1)|(1<<z+y-1)|(1<<(x+y+z-1));
	state=(1<<x+y+z)-1;
	dp[0][0]=1;
	for (int i=1;i<=n;i++)
	  for (int j=0;j<=state;j++)
	    {
		  if (dp[i-1][j]==0)
		   continue;
		  for (int k=1;k<=10;k++)
		    {
			int noww=(j<<k)|(1<<k-1);
			noww=noww&state;
			if ((noww&st)!=st)
			 dp[i][noww]=(dp[i][noww]+dp[i-1][j])%si; 
			}
		}
	for (int i=0;i<=state;i++)
	  ans=(ans-dp[n][i]+si)%si;
	cout<<ans<<endl;
	return 0;
}