#! /usr/bin/perl

use Algorithm::Combinatorics q(:all);
use Data::Dump;
use strict;
use warnings;
push @ARGV, (6, 4);     # default (n, k)

# recursive formula
#
sub choose {
    my ($n, $k) = @_;
    !$n ? ([$k]) x !$k : map [@$_, $k], choose($n-1, $k), choose($n-1, $k-1)
}

dd choose(@ARGV);

# iterator version
#
sub pinball_iter {
    my ($n, $k) = @_;
    my $iter = combinations([1 .. $n], $k);

    sub {
        my @path = (0);
        $path[$_]++ for @{ $iter->next() // return };
        $path[$_]+=$path[$_-1] for (1 .. $n);
        return \@path;
    }
}

my $it = pinball_iter(@ARGV);
while (my $x = $it->()) {
    dd $x;
}

##</code><code>##

sub choose {
    my ($n, $k) = @_;
    !$n ? (["$n-$k"]) x !$k
        : map [@$_, "$n-$k"], choose($n-1, $k), choose($n-1, $k-1)
}