Background

Due to differences in the performance of judging machines, the original time limit was 6 s, and the Luogu time limit is 9 s.

Problem Description

Xiao Y and Xiao C are playing a game.

A positive fraction is defined as an irreducible fraction whose numerator and denominator are both positive integers.

A perfect positive fraction set $S$ is 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 $x\in S$ and $x>2$, $x-2 \in S$.

It can be proven that the above 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 $f(i,j)$ indicate whether $\dfrac{i}{j}$ is a perfect positive fraction. That is, $f(i,j)=1$ 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 whose numerator does not exceed $n$ and denominator does not exceed $m$, that is, compute $\sum_{i=1}^n \sum_{j=1}^m f(i,j)$.

As time goes by, Xiao C and Xiao Y will meet again. Looking back, everyone has lived the life they wanted.

Input Format

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

Output Format

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

10 10

16

见 fraction2.in/ans
这个样例满足测试点 4-6 的约束条件

见 fraction3.in/ans
这个样例满足测试点 11-14 的约束条件

见 fraction4.in/ans
这个样例满足测试点 15-17 的约束条件

Hint

[Sample 1 Explanation]

It can be proven that there are $16$ perfect positive fractions with both numerator and denominator not exceeding $10$. The $8$ that are less than $1$ are:

• $\dfrac{1}{2},\dfrac{1}{4},\dfrac{1}{6},\dfrac{1}{8},\dfrac{1}{10},\dfrac{2}{5},\dfrac{2}{9},\dfrac{4}{9}$.

The $8$ perfect positive fractions greater than $1$ are the reciprocals of the above $8$ perfect positive fractions less than $1$.

• You can verify whether $\dfrac{2}{9}$ is a perfect positive fraction as follows: since $\dfrac{1}{2}\in S$, $\dfrac{1}{2}+2=\dfrac{5}{2}\in S$, $\dfrac{5}{2}+2=\dfrac{9}{2}\in S$, $\dfrac{1}{\dfrac{9}{2}}=\dfrac{2}{9}\in S$;
• You can verify whether $\dfrac{3}{7}$ is a perfect positive fraction as follows: assume $\dfrac{3}{7}$ 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. Therefore, $\dfrac{3}{7}$ is not a perfect positive fraction.

[Constraints]

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

::cute-table{tuack}

Translated by ChatGPT 5