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B - Sum of Three Integers

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.

2 2

6

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

• $X = 0, Y = 0, Z = 2$
• $X = 0, Y = 2, Z = 0$
• $X = 2, Y = 0, Z = 0$
• $X = 0, Y = 1, Z = 1$
• $X = 1, Y = 0, Z = 1$
• $X = 1, Y = 1, Z = 0$

5 15

1

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