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: Runtime Error)

#include<iostream>
#include<map>
#include<string>
#include<vector>
#include<algorithm>
using namespace std;
long long X, Y, Z, n, power[50], mod = 1000000007;
int M[42][262144], GO[262144][10];

string parse(int r, int bit) {
	int cnt = 1, c = -1; string Y = "";
	for (int i = 0; i < r; i++) {
		if ((bit & (1 << i)) != 0)c = i;
	}
	r = c + 1;
	for (int i = 0; i < r; i++) {
		if ((bit & (1 << i)) != 0) { Y += ('0' + cnt); cnt = 1; }
		else cnt++;
	}
	return Y;
}
int parse2(int r, string Y) {
	int cnt = 0, t = 0;
	for (int i = 0; i < Y.size(); i++) {
		t += (Y[i] - '0'); cnt += (1 << (t - 1));
	}
	return cnt;
}
long long solve(int depth, int bit) {
	if (M[depth][bit] >= 0)return M[depth][bit];
	string S = parse(X + Y + Z, bit);

	int G = 0, R = 0;
	for (int i = S.size() - 1; i >= 0; i--) {
		G += (S[i] - '0');
		if (G == X || G == X + Y || G == X + Y + Z)R++;
	}
	if (R == 3) {
		M[depth][bit] = power[n - depth];
		return power[n - depth];
	}
	if (depth == n) { M[depth][bit] = 0; return 0; }

	long long cnt = 0;
	for (int i = 1; i <= 10; i++) {
		int P = GO[bit][i];
		cnt += solve(depth + 1, P); cnt %= mod;
	}
	M[depth][bit] = cnt;
	return cnt;
}
int main() {
	cin >> n >> X >> Y >> Z;
	for (int i = 0; i <= n; i++) { for (int j = 0; j < (1 << (X + Y + Z)); j++) { M[i][j] = -1; } }
	for (int i = 0; i < (1 << (X + Y + Z)); i++) {
		for (int j = 1; j <= 10; j++) {
			string A = parse(X + Y + Z, i); A += ('0' + j);
			int V = 0, C = 0; for (int k = 0; k < A.size(); k++)V += (A[k] - '0');
			if (j >= 8) { V = 0; A = ""; }
			while (V > X + Y + Z) { V -= (A[C] - '0'); C++; }
			A = A.substr(C, A.size() - C);
			GO[i][j] = parse2(X + Y + Z, A);
		}
	}
	power[0] = 1; for (int i = 1; i < 50; i++)power[i] = power[i - 1] * 10 % mod;
	cout << solve(0, 0) << endl;
	return 0;
}