Problem Description

Translated from ROIR 2020 Day2 T2. Планировка участка, translated by Alpha1022.

Translator’s note: Since the original statement was a bit hard for the translator to understand, the meaning is abstracted directly here.

You have four variables $a,b,c,d$ that must satisfy:

• $a,b,c,d \in \mathbb N^*$.
• $a \ne x, b \ne x$.
• $a > c, b > d$.
• $a \cdot b - c \cdot d = n$.

For given $x,n$, find how many possible assignments of $a,b,c,d$ there are.

Input Format

The first line contains two integers $n,x$.
If $x=0$, it means the second condition is ignored.

Output Format

One line, the number of valid assignments of $a,b,c,d$.

3 0

1

5 0

5

5 3

2

Hint

Sample 1 Explanation

Only $a=2,b=2,c=1,d=1$ is valid.

Sample 2 Explanation

The following assignments are valid:

• $a=2,b=3,c=1,d=1$;
• $a=2,b=4,c=1,d=3$;
• $a=3,b=2,c=1,d=1$;
• $a=3,b=3,c=2,d=2$;
• $a=4,b=2,c=3,d=1$.

Sample 3 Explanation

The following assignments are valid:

• $a=2,b=4,c=1,d=3$;
• $a=4,b=2,c=3,d=1$.

Constraints

For $100\%$ of the testdata, $1 \le n \le 3000, 0 \le x \le 3000$.
The detailed limits are shown in the table below:

Translated by ChatGPT 5