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 PHP7 (7.0.15) (judge verdict: Time Limit Exceeded)

<?php
  $input = explode(" ", fgets(STDIN));
  $K = $input[0];
  $S = $input[1];
  $count = 0; 
  $i = $K;
  $j = $K;
  $k = $K;
  
  $mix = $i + $j + $k;
  if($mix < $S){
    echo 0;
    exit();
  }

  elseif($i + $j + $k == $S){
    echo 1;
    exit();
  }

  for($i=$K;$i>=0;$i--){
	  if($i == $S && $j == 0 && $k == 0){
      $count++;
      continue;
    }
    elseif($i > $S){
      continue;
    }

    for($j=$K;$j>=0;$j--){
      if($i + $j == $S && $k == 0){
        $count++;
        continue;
      }
      elseif($i + $j > $S){
        continue;            
      }
      for($k=$K;$k>=0;$k--){
        
        if($i + $j + $k == $S){
          $count++;
          continue;
        }
        elseif($i + $j + $k > $S){
          continue;
        }
      }	 
    }
  }
  echo $count;
?>