Problem Description

Xiao Y and Xiao C are playing a game.

A positive fraction is defined as a fraction where both the numerator and the denominator are positive integers and the fraction is in its simplest form.

A perfect positive fraction set $S$ is defined as a set of positive fractions that satisfies the following five properties:
- $\dfrac{1}{2} \in S$;
- For $\dfrac{1}{2} < x < 2$, $x \not \in S$;
- For all $x \in S$, $\dfrac{1}{x} \in S$;
- For all $x \in S$, $x + 2 \in S$;
- For all $x \in S$ where $x > 2$, $x - 2 \in S$;

It can be proven that these five properties uniquely determine the perfect positive fraction set $S$.

All positive fractions in the perfect positive fraction set $S$ are called perfect positive fractions. Let $f(i,j)$ denote whether $\dfrac{i}{j}$ is a perfect positive fraction, i.e., $f(i,j) = 1$ if and only if $i$ and $j$ are coprime and $\dfrac{i}{j} \in S$, otherwise $f(i,j) = 0$.

Xiao C asks Xiao Y: Given $n, m$, find the number of perfect positive fractions where the numerator does not exceed $n$ and the denominator does not exceed $m$, i.e., find $\sum_{i=1}^n \sum_{j=1}^m f(i,j)$.

Input Format

The first line of input contains two positive integers $n$ and $m$, representing the ranges of the numerator and the denominator, respectively.

Output Format

Output a single line containing a non-negative integer, representing the corresponding answer.

Sample Input and Output

Sample Input #1

10 10

Sample Output #1

16

Sample Input #2

See fraction2.in/ans
This sample satisfies the constraints of test points 4-6

Sample Output #2

Sample Input #3

See fraction3.in/ans
This sample satisfies the constraints of test points 11-14

Sample Output #3

Sample Input #4

See fraction4.in/ans
This sample satisfies the constraints of test points 15-17

Sample Output #4

Notes/Hints

[Sample 1 Explanation]

It can be proven that there are 16 perfect positive fractions with both numerator and denominator not exceeding 10, with 8 of them being less than 1 as follows:
- $\dfrac{1}{2}, \dfrac{1}{4}, \dfrac{1}{6}, \dfrac{1}{8}, \dfrac{1}{10}, \dfrac{2}{5}, \dfrac{2}{9}, \dfrac{4}{9}$.

The 8 perfect positive fractions greater than 1 are the reciprocals of the above 8 fractions less than 1.
- Verification of $\dfrac{2}{9}$ being a perfect positive fraction: Since $\dfrac{1}{2} \in S$, $\dfrac{1}{2} + 2 = \dfrac{5}{2} \in S$, $\dfrac{5}{2} + 2 = \dfrac{9}{2} \in S$, $\dfrac{1}{\dfrac{9}{2}} = \dfrac{2}{9} \in S$;
- Verification of $\dfrac{3}{7}$ not being a perfect positive fraction: Assuming $\dfrac{3}{7}$ is a perfect positive fraction, then $\dfrac{1}{\dfrac{3}{7}} = \dfrac{7}{3} \in S$, $\dfrac{7}{3} - 2 = \dfrac{1}{3} \in S$, $\dfrac{1}{\dfrac{1}{3}} = 3 \in S$, $3 - 2 = 1 \in S$, which contradicts the second property, thus $\dfrac{3}{7}$ is not a perfect positive fraction.

[Data Range]

For all test data, it is guaranteed that $2 \leq n, m \leq 3 \times 10^7$.

见题面 Input 部分

见题面 Output 部分