Here's one idea for an algorithm. Getting the output into the @want_output array is left up to you.

#!/usr/bin/perl

# https://perlmonks.org/?node_id=11102502

use strict;
use warnings;

my @input = qw/ 2 5 7 /;
my $target = 15;

print "\ntarget $target from @input\n";
find( 0, [], $target, @input );
print "That's all, folks\n";

$target = 3;

print "\ntarget $target from @input\n";
find( 0, [], $target, @input );
print "That's all, folks\n";

$target = 35;

print "\ntarget $target from @input\n";
find( 0, [], $target, @input );
print "That's all, folks\n";

sub find
  {
  my ($sum, $sofar, $want, @numbers ) = @_;
  if( $sum == $want )
    {
    print "@$sofar\n";
    }
  elsif( $sum < $want and @numbers and $numbers[0] > 0 )
    {
    find( $sum + $numbers[0], [ @$sofar, $numbers[0] ], $want, @number
+s );
    find( $sum, $sofar, $want, @numbers[1..$#numbers] );
    }
  }
[download]

Outputs:

target 15 from 2 5 7
2 2 2 2 2 5
2 2 2 2 7
5 5 5
That's all, folks

target 3 from 2 5 7
That's all, folks

target 35 from 2 5 7
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 5
2 2 2 2 2 2 2 2 2 2 2 2 2 2 7
2 2 2 2 2 2 2 2 2 2 5 5 5
2 2 2 2 2 2 2 2 2 5 5 7
2 2 2 2 2 2 2 2 5 7 7
2 2 2 2 2 2 2 7 7 7
2 2 2 2 2 5 5 5 5 5
2 2 2 2 5 5 5 5 7
2 2 2 5 5 5 7 7
2 2 5 5 7 7 7
2 5 7 7 7 7
5 5 5 5 5 5 5
7 7 7 7 7
That's all, folks
[download]