#!/usr/bin/perl -w
use strict;
use Algorithm::Loops qw( NestedLoops );
$| = 1;

my @sum= shift || 20;
my $terms = shift || 4;

print "Ways to get a sum of $sum[0] from $terms unique addends:\n";

my $tries= 0;
my $iter= NestedLoops(
    [ ( sub {
            my $n = @_ ? 1+$_[-1] : 1;
            my $t = $terms - @_;
            my $m = $sum[$#_]/$t-($t-1)/2;
            return [ $n .. int $m ];
    } ) x $terms ],
    {
        OnlyWhen => sub {
            $tries++;
                0 == ( $sum[@_]= $sum[$#_] - $_[-1] )
            &&  $terms == @_;
        },
    },
);
my @cnt;
my $seq= 0;
while(  @cnt= $iter->()  ) {
    printf "%d) %s\n", ++$seq, join ' + ', @cnt
}
print "($tries tries)\n";