Problem:
Score : 200 points

Problem Statement

You are given two integers K and S.

Three variable X, Y and Z takes integer values satisfying 0≤X,Y,Z≤K.

How many different assignments of values to X, Y and Z are there such that X + Y + Z = S?

Constraints

2≤K≤2500

0≤S≤3K

K and S are integers.

Input

The input is given from Standard Input in the following format:

K S

Output

Print the number of the triples of X, Y and Z that satisfy the condition.

Sample Input 1

2 2

Sample Output 1

6

There are six triples of X, Y and Z that satisfy the condition:

X = 0, Y = 0, Z = 2

X = 0, Y = 2, Z = 0

X = 2, Y = 0, Z = 0

X = 0, Y = 1, Z = 1

X = 1, Y = 0, Z = 1

X = 1, Y = 1, Z = 0

Sample Input 2

5 15

Sample Output 2

1

The maximum value of X + Y + Z is 15, achieved by one triple of X, Y and Z.

Solution in Perl (v5.18.2) (judge verdict: Accepted)

#! usr/bin/perl

use strict;
use warnings;

sub max {
    my ($a,$b)=@_;
    $a>$b ? $a : $b;    
}

chomp(my $line = <STDIN>);
my ($K,$S) = split ' ',$line;

my $count=0;
foreach my$x(0..$S/3) {
    foreach my$y(max($x,$S-$x-$K)..($S-$x)/2) {
        my $z = $S-$x-$y;
        if (($x==$y)&&($y==$z)) {$count += 1;next};
        if (($x==$y)||($y==$z)) {$count += 3;next};
        $count += 6;
    }
}

print "$count\n"