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;
use std::cmp;
use std::collections::BinaryHeap;
use std::collections::HashMap;
use std::collections::HashSet;

fn read_line() -> String {
    let mut buf = String::new();
    io::stdin().read_line(&mut buf).ok();
    buf
}

static MOD: u64 = 1_000_000_007;

fn main() {
    let line: Vec<usize> = read_line().split_whitespace().map(|s| s.parse().unwrap()).collect();
    let n = line[0];
    let x = line[1];
    let y = line[2];
    let z = line[3];

    let mut memo = vec![vec![0u64; 1 << 16]; n+1];
    memo[0][0] = 1;
    
    let mut memo2 = vec![true; 1 << 17];
    for i in 0..1 << 17 {
        let mut state = 0;
        let mut sum = 0;
        let mut pos = 0;
        let mut prev = 0;
        while pos < 17 {
            if (i & (1 << pos)) > 0 {
                sum += pos-prev+1;
                prev = pos+1;
                if state == 0 && sum == z {
                    state = 1;
                    sum = 0;
                } else if state == 1 && sum == y {
                    state = 2;
                    sum = 0;
                } else if state == 2 && sum == x {
                    state = 3;
                    break;
                }
            }
            pos += 1;
        }
        
        if state == 3 {
            memo2[i] = false;
        }
    }
    
    for i in 0..n {
        for j in 0..1 << 16 {
            // println!("len: {}, state: {:b}, sum: {}", i, j, memo[i][j]);
            if !memo2[j] {
                continue;
            }
            for k in 1..11 {
                let next = ((j << k) + (1 << (k-1))) % (1 << 17);
                if memo2[next] {
                    memo[i+1][next % (1 << 16)] += memo[i][j];
                    memo[i+1][next % (1 << 16)] %= MOD;
                }
            }
        }
    }
    let mut ans = 1u64;
    for i in 0..n {
        ans *= 10;
        ans %= MOD;
    }

    for i in 0..1 << 16 {
        ans += MOD - memo[n][i];
        ans %= MOD;
    }

    println!("{}", ans);
}