Score : $400$ points

Problem Statement

Given are integers $N$ and $K$. How many quadruples of integers $(a,b,c,d)$ satisfy both of the following conditions?

• $1 \leq a,b,c,d \leq N$
• $a+b-c-d=K$

Constraints

• $1 \leq N \leq 10^5$
• $-2(N-1) \leq K \leq 2(N-1)$
• All numbers in input are integers.

Input

Input is given from standard input in the following format:

$N$ $K$

Output

Print the answer.

2 1

4

Four quadruples below satisfy the conditions:

• $(a,b,c,d)=(2,1,1,1)$
• $(a,b,c,d)=(1,2,1,1)$
• $(a,b,c,d)=(2,2,2,1)$
• $(a,b,c,d)=(2,2,1,2)$

2525 -425

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