Quarantine Math

Time limit1.25sMemory limit256 MB

Summary

Given n and m up to 1e9, sum the divisor counts of all positive k with (n mod k) + (m mod k) >= k, using number theory.

Level: Hard8 of 10
Topics: Number theory, Math, Brute force, Implementation
Solved: No attempts yet

Problem

It's quarantine and you're so bored that you decided to dedicate some time to level up your math skills. Unfortunately, yesterday you bumped into a problem you couldn't solve. However, you've dreamt of this problem for the entire night, so maybe today the luck will be on your side?

For given natural numbers $n$ , $m$ , let $S(n, m)$ be a set of positive integers such that for every element $k$ in this set, $(n \bmod k) + (m \bmod k) \ge k$ , where $a \bmod b$ is the remainder of $a$ divided by $b$ .

The problem asks to compute the value of the following function: $F(n, m) = \sum\_{k \in S\_{(n,m)}}{D(k)}$ where $D(x)$ is the number of positive divisors of the number $x$ .

Input

Two natural numbers $n$ , $m$ . $1 \le n, m \le 10^9$ .

Output

One number: the value of the function $F(n, m)$ .

Hint

$S(4, 7) = 5, 8, 9, 10, 11$ , $D(5) = 2$ , $D(8) = 4$ , $D(9) = 3$ , $D(10) = 4$ , $D(11) = 2$

Examples1

Example 1
Input
```
4 7
```
Expected output
```
15
```