use strict;
use warnings;
use bigint;

#  e*x-1 = -b*(p-1)*(q-1)

# pq = 320353134631681309556473161605063339987 * 276065138433109647164739983515002720659
#my $pq= 88438332459575713003174419268502556144700924300208596763704599584326505691433;
#my $x= 69399065592429616374372553429979240083906900467887630575728849318636934515345;
#  factor e*x-1 = 4548206561731059768327254034140549457379006535963951645041541597795508777332165264
#my @f= reverse qw(2 2 13 23 43 35941363 3174776518993 17508453722537147 50452863802409212925407001 219350806857289);
my $pq= 96436236649188001138471945066857677842570427201821167402703570072037925931699;
my $x= 26839753978381511829435712315478035977190439224674628583719899884502784648193;
my $e= 0x10001;
#  omitted 2^10
my @f= reverse qw(2 3 5 19 71359 85451 38156773220407 50972760339314981329 508211599216931138498916563746223);

my $tst= getnum(\@f, 0, 0);
print "tst=$tst\n";
my $t0= time();
my $mx= 3**@f;
for (my $i=0 ; $i<$mx ; $i++) {
    my $b= getnum(\@f, $i, 0);
    my $p= 2*getnum(\@f, $i, 1)+1;
    my $q= 2*getnum(\@f, $i, 2)+1;
    if ($p*$q==$pq) {
        print "p=$p\nq=$q\n";
        last;
    }
    if (($i%2000)==1999) {
        my $t= time();
        my $r= $i/($t-$t0);
        printf("%10d %8d  %8.2f  %8d\n", $t, $i, $r, ($mx-$i)/$r);
    }
}

sub getnum {
    my ($f, $i, $n)= @_;
    my $num= 1;
    for (my $j= 0 ; $j<@$f ; $j++) {
        my $m= $i%3; $i = int($i/3);
        $num *= $f->[$j] if ($m==$n);
    }
    return $num;
}