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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

N, X, Y, Z = gets.split.map(&:to_i)
STATE = 2**(X+Y+Z)
MASK = STATE - 1
MOD = 10**9+7

dp = Array.new(N+1){Array.new(STATE, 0)}
dp[0][0] = 1
N.times do |i|
    STATE.times do |bits|
        next if dp[i][bits] == 0
        (1..10).each do |d|
            new_bits = MASK & ((bits<<d) + (1<<(d-1)))
            unless new_bits[Z-1] == 1 && new_bits[Y+Z-1] == 1 && new_bits[X+Y+Z-1] == 1
                dp[i+1][new_bits] += dp[i][bits]
                dp[i+1][new_bits] %= MOD
            end
        end
    end
end

sum = dp[N].inject(:+)
puts (10**N - sum) % MOD