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 defined as a set of positive fractions satisfying the following five properties:

1. $\frac{1}{2} \in S$;
2. For $\frac{1}{2} < x < 2$, $x \notin S$;
3. For all $x \in S$, $\frac{1}{x} \in S$;
4. For all $x \in S$, $x + 2 \in S$;
5. For all $x \in S$ and $x > 2$, $x - 2 \in S$.

It can be proven that the five properties above determine a unique 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 $\frac{i}{j}$ is a perfect positive fraction, i.e., $f(i, j) = 1$ if and only if $i$ and $j$ are coprime and $\frac{i}{j} \in S$, otherwise $f(i, j) = 0$.

Xiao C asks Xiao Y: Given $n$ and $m$, find the number of perfect positive fractions with numerator at most $n$ and denominator at most $m$, i.e., calculate $\sum_{i=1}^{n} \sum_{j=1}^{m} f(i, j)$.

Input

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

Output

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

Examples

Input 1

10 10

Output 1

16

Note 1

It can be proven that there are 16 perfect positive fractions with numerator and denominator both at most 10. The 8 fractions less than 1 are as follows: $\frac{1}{2}, \frac{1}{4}, \frac{1}{6}, \frac{1}{8}, \frac{1}{10}, \frac{2}{5}, \frac{2}{9}, \frac{4}{9}$. The 8 perfect positive fractions greater than 1 are the reciprocals of the 8 perfect positive fractions less than 1 listed above.

• $\frac{2}{9}$ can be verified as a perfect positive fraction as follows: since $\frac{1}{2} \in S$, $\frac{1}{2} + 2 = \frac{5}{2} \in S$, $\frac{5}{2} + 2 = \frac{9}{2} \in S$, and $\frac{1}{9/2} = \frac{2}{9} \in S$, therefore $\frac{2}{9}$ is a perfect positive fraction.
• $\frac{3}{7}$ can be verified as a perfect positive fraction as follows: assume $\frac{3}{7}$ is a perfect positive fraction, then $\frac{1}{3/7} = \frac{7}{3} \in S$, $\frac{7}{3} - 2 = \frac{1}{3} \in S$, $\frac{1}{1/3} = 3 \in S$, $3 - 2 = 1 \in S$, which contradicts the second property. Therefore, $\frac{3}{7}$ is not a perfect positive fraction.

Examples 2-4

See the files fraction/fraction2.in and fraction/fraction2.ans, fraction/fraction3.in and fraction/fraction3.ans, and fraction/fraction4.in and fraction/fraction4.ans in the contestant directory. These examples satisfy the constraints for test cases 4–6, 11–14, and 15–17, respectively.

Constraints

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