<?php

function weak_compositions($nboxes, $nballs, $parent="", $nested=0) {
      $one = $nested ? "1" : "";
      if ($nboxes > 1) {
        for ($i = 0; $i <= $nballs; $i++) {
      weak_compositions($nboxes - 1, $i, $parent . $one . str_repeat("0", $nballs - $i), 1);
        }
      } else {
        echo $parent . $one .  str_repeat("0", $nballs) . "\n";
      }
    }

$f=5;
$c=2;
weak_compositions($c+1, $f-$c);

?>