407001: GYM102672 I Tennis score

Aurora and Knotgrass decided to play tennis and asked Thistlelwit to be the judge. At the start the score was $$$0 : 0$$$. Then, a few times the score increased by $$$1$$$. The game ended with the score $$$a : b$$$.

Thistlelwit was bored so she counted the sum of the gcds of the players' scores after each score change. the gcd  — is the greatest divisor of two numbers. For example, the game could go as follows:

• $$$0 : 0$$$
• $$$1 : 0$$$, $$$\textrm{gcd}(1, 0) = 1$$$
• $$$2 : 0$$$, $$$\textrm{gcd}(2, 0) = 2$$$
• $$$2 : 1$$$, $$$\textrm{gcd}(2, 1) = 1$$$
• $$$2 : 2$$$, $$$\textrm{gcd}(2, 2) = 2$$$
• $$$2 : 3$$$, $$$\textrm{gcd}(2, 3) = 1$$$

In that case, Thistlelwit would get $$$1 + 2 + 1 + 2 + 1 = 7$$$.

After the end of the game Thistlelwit got curious about what minimal number she could potentially get. Please, help her calculate that number.

The first line contains two integers $$$a$$$ and $$$b$$$ — the final scores of Aurora and Knotgrass ($$$0 \le a, b \le 10^9$$$).

Output one number  — the minimal score which Thistlelwit could get.

2 1

3

4 6

11

0 0

0

10 10

31