Inspired by this glove-themed 538 Riddler Express Puzzle.

##Task You are given a positive integer n, and a list A = [a_1, a_2, ..., a_k] of k distinct positive integers.

Then a restricted composition is an ordered list P = [p_1, p_2, ..., p_m] where each p_i is a (not necessarily distinct) member of A, and p_1 + p_2 + ... + p_m = n.

So, if n = 10, and A = [2,3,4] then an example of a restricted composition would be P = [3,4,3]. Another example would be P = [2,3,3,2]. A third example would be P = [3,3,4]. But there's no restricted composition that starts [3,3,3,...], because 10-(3+3+3) = 1, which is not in A.

We want the total number of different restricted compositions given the inputs, as an integer.

##Inputs

A positive integer n and a list A of distinct positive integers. All reasonable input formats allowed.

##Output

The number of distinct restricted compositions.

##Terms and Conditions

This is code-golf; and thus we seek the shortest submissions in bytes satisfying the constraints. Any use of the usual loopholes voids this contract.

##Test Cases

(5, [2, 3, 4]) => 2 (10, [2, 3, 4]) => 17 (15, [3, 5, 7]) => 8 

Inspired by this glove-themed 538 Riddler Express Puzzle.

Task

You are given a positive integer n, and a list A = [a_1, a_2, ..., a_k] of k distinct positive integers.

Then a restricted composition is an ordered list P = [p_1, p_2, ..., p_m] where each p_i is a (not necessarily distinct) member of A, and p_1 + p_2 + ... + p_m = n.

So, if n = 10, and A = [2,3,4] then an example of a restricted composition would be P = [3,4,3]. Another example would be P = [2,3,3,2]. A third example would be P = [3,3,4]. But there's no restricted composition that starts [3,3,3,...], because 10-(3+3+3) = 1, which is not in A.

We want the total number of different restricted compositions given the inputs, as an integer.

Inputs

A positive integer n and a list A of distinct positive integers. All reasonable input formats allowed.

Output

The number of distinct restricted compositions.

Terms and Conditions

This is code-golf; and thus we seek the shortest submissions in bytes satisfying the constraints. Any use of the usual loopholes voids this contract.

Test Cases

(5, [2, 3, 4]) => 2 (10, [2, 3, 4]) => 17 (15, [3, 5, 7]) => 8