Inspired by this glove-themed 538 Riddler Express Puzzle.
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
p_1 + p_2 + ... + p_m = n.
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
10-(3+3+3) = 1, which is not in
We want the total number of different restricted compositions given the inputs, as an integer.
A positive integer
n and a list
A of distinct positive integers. All reasonable input formats allowed.
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.
(5, [2, 3, 4]) => 2 (10, [2, 3, 4]) => 17 (15, [3, 5, 7]) => 8