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)

#include <bits/stdc++.h>

#define For(i, j, k) for (int i = j; i <= k; ++ i)
#define Forr(i, j, k) for (int i = j; i >= k; -- i)

using namespace std;

inline void File() {
	freopen("E.in", "r", stdin);
	freopen("E.out", "w", stdout);
}

const int N = 42, M = (1 << 17) + 5, mod = 1e9 + 7;
int dp[N][M], n, z, y, x, ans;

int main() {

	cin >> n >> x >> y >> z;

	int all = (1 << x + y + z) - 1,
		fbd = (1 << x - 1) | (1 << x + y - 1) | (1 << x + y + z - 1);

	dp[0][0] = 1, ans = 1;
	
	For(i, 1, n) {
		ans = 10ll * ans % mod;
		For(st, 0, all) For(k, 1, 10) {
			int nw = ((1 << k - 1) | (st << k)) & all;
			if ((nw & fbd) ^ fbd) 
				dp[i][nw] = (dp[i][nw] + dp[i - 1][st]) % mod;
		}
	}

	For(i, 0, all) ans = (ans - dp[n][i] + mod) % mod;

	cout << ans << endl;
	return 0;
}