use Memoize;
memoize 'restricted_partitions';

sub restricted_partitions {
    my ($N, @coins) = @_;

    ## can't do it if $N is negative (might get called with $N<0 if
    ##    we have coins bigger than $N)
    ## only one way to make change for 0
    return 0 if $N < 0;
    return 1 if $N == 0;

    ## pick any available coin to be the coin with the lowest ID in this
    ## partition. once we pick that, we have left to partition $N-$coin,
    ## and can't use coins with lower IDs to do it...

    my $total = 0;
    for (0 .. $#coins) {
        $total += restricted_partitions($N-$coins[$_], @coins[$_ .. $#coins]);
    }
    return $total;
}

print restricted_partitions(@ARGV), $/;