Site Planning

Scientists are planning a site for a testing ground. The site must be an $a \times b$ rectangle, and the testing ground must be a $c \times d$ rectangle. The scientists have not settled on the exact values of $a$, $b$, $c$, and $d$, but they know the following.

• The side lengths $a, b, c, d$ must be positive integers expressed in kilometers.
• For the safety of the experiment, the width and height of the site must differ from $x$, that is, $a \neq x$ and $b \neq x$ must hold.
• The site will be enclosed by a fence, and the testing ground must fit entirely inside the site, that is, $a > c$ and $b > d$ must hold.
• The area of the site not occupied by the testing ground must be exactly $n$ square kilometers, that is, $a \cdot b - c \cdot d = n$ must hold.

The scientists want to know how many ways they can choose suitable values of $a$, $b$, $c$, and $d$. Write a program that, given $n$ and $x$, determines the number of ways to choose $a$, $b$, $c$, and $d$ so that all the conditions above hold.

The first line of input contains two numbers: $n$, the area of the free part of the site without the testing ground $(1 \le n \le 3000)$, and $x$, the forbidden side length of the site $(0 \le x \le 3000)$.

A value of $x = 0$ means there are no restrictions on the side lengths, since the side lengths must be positive integers and therefore greater than 0.

On a single line, output the number of ways to choose $a$, $b$, $c$, and $d$ so that all the conditions hold.

In the first test example, only $a = 2, b = 2, c = 1, d = 1$ fits the conditions.

In the second test example, the following fit the conditions.

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

In the third test example, the following fit the conditions.

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

In the remaining answers from the previous test, either $a$ or $b$ equals 3.