Sum of Three Integers

AtCoder

IDabc051_b

Time2000ms

Memory256MB

Difficulty—

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: $K$ $S$ [samples]

Samples

Input #1

2 2

Output #1

6

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

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

Input #2

5 15

Output #2

1

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

API Response (JSON)

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      "description_type": "Markdown"
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      "content": "You are given two integers $K$ and $S$.  \nThree variable $X, Y$ and $Z$ takes integer values satisfying $0≤X,Y,Z≤K$.  \nHow many different assignments of values to $X, Y$ and $Z$ are there such that $X...",
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