foreach my $i( reverse 1..$len){
        my $x = 10 * $a[$i-1] + $q * $i;
        $a[$i-1] = $x % (2 * $i - 1);
        $q = int($x / (2 * $i - 1));
    }

##</code><code>##

    foreach my $i( reverse 0 .. $len-1){
        my $x = 10 * $a[$i] + $q * ($i+1);
        my $divisor = 2 * $i + 1;
        $a[$i] = $x % $divisor;
        $q = int($x / $divisor);
    }