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::stdin;
use std::str::FromStr;

fn main(){
    let mod_ = 1_000_000_007;
    let nxyz: Vec<usize> = get_vec();
    let (n, x, y, z) = (nxyz[0], nxyz[1], nxyz[2], nxyz[3]);
    let g = 1 << 16;
    let mut dp = vec![vec![0;g];n+1];
    dp[0][0] = 1;

    let v = validator(x, y, z);

    for i in 0..n {
        for j in 0..10 {
            for k in 0..g {
                let a = ((k << 1) + 1) << j;
                if ok(a, v) {
                    dp[i+1][a%g] += dp[i][k];
                    dp[i+1][a%g] %= mod_;
                }
            }
        }
    }

    let mut m: i64 = 1;
    for _ in 0..n {
        m *= 10;
        m %= mod_;
        m += mod_;
    }

    println!("{}", (m - dp[n].iter().fold(0, |acc, x| (acc+x)%mod_) + mod_) % mod_);

}

fn validator(x: usize, y: usize, z: usize) -> usize {
    let mut v = 1;
    v = v << x;
    v += 1;
    v = v << y;
    v += 1;
    v = v << z;
    v >> 1
}

fn ok(a: usize, v: usize) -> bool{
    v != (a & v)
}

#[allow(dead_code)]
fn get_line() -> String {
    let mut s = String::new();
    match stdin().read_line(&mut s){
        Ok(_) => {s.trim().to_string()}
        Err(_) => String::new()
    }
}

#[allow(dead_code)]
fn get_vec<T: std::str::FromStr>() -> Vec<T> {
    let line = get_line();
    line.split_whitespace().filter_map(|x| x.parse().ok()).collect()
}

#[allow(dead_code)]
fn get_one<T: FromStr + Copy>() -> T {
    let v = get_vec();
    v[0]
}

#[allow(dead_code)]
fn get_pair<T: FromStr + Copy>() -> (T, T) {
    let v = get_vec();
    (v[0], v[1])
}

#[allow(dead_code)]
fn get_triple<T: FromStr + Copy>() -> (T, T, T) {
    let v = get_vec();
    (v[0], v[1], v[2])
}

#[allow(dead_code)]
fn get_chars() -> Vec<char> {
    get_line().chars().collect()
}