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 Rust (1.15.1) (judge verdict: Accepted)

use std::io::BufRead;

const P: u64 = 1_000_000_007;

fn main() {
    let stdin = std::io::stdin();
    let val = stdin.lock().gets().split(' ')
        .map(|x| x.parse().unwrap()).collect::<Vec<usize>>();
    let (n, x, y, z) = (val[0], val[1], val[2], val[3]);

    let size = 1 << (x + y + z);
    let entry = 1 << (x + y + z);
    assert!(entry != 0);
    let goal = ((entry >> x | entry) >> y | entry) >> z;
    let mut state = vec![0; size];
    state[0] = 1;
    let mut count = 0;
    for _ in 0..n {
        count = count * 10 % P;
        let mut next = vec![0; size];
        for d in 1..11 {
            for s in 0..size {
                let s2 = (s | entry) >> d;
                if (s2 & goal) == goal {
                    count += state[s];
                } else {
                    next[s2] += state[s];
                }
            }
        }
        state = next;
        for s in state.iter_mut() {
            *s %= P;
        }
    }
    println!("{}", count % P);
}

trait Gets { fn gets(&mut self) -> String; }
impl<T: std::io::BufRead> Gets for T {
    fn gets(&mut self) -> String { self.lines().next().unwrap().unwrap() } }