Sum of Three Integers

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Problem type
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.


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