use strict;
use warnings;
use Math::Polynomial;
use Data::Dumper;


#points to interpolate tghrough
#(x,y)
my @points = @ARGV;
my @pair_points;



#the followin line is only for debugging
@points = ( 1,3,5,9,20,30) ;


while ( scalar @points ) {
	push @pair_points , [ pop @points , pop @points ];
}





sub P_j {
	my $n  =  scalar @points / 2;
	my $j = shift;
	my $pol = Math::Polynomial->new(1);
	$pol *= $pair_points[$j]->[1];
	for( my $k = 0 ; $k < $n ; $k++ ) {
		my $generic_pol =	Math::Polynomial->new( 1, -$pair_points[$k]->[0] ) /
							( $pair_points[$j]->[0] - $pair_points[$k]->[0])
							unless $k == $j;
		$pol *= $generic_pol;
	}
	return $pol;
}



print P_j 4;