The Lost Cow

Farmer John has lost his prize cow Bessie, and he needs to find her!

Fortunately, there is only one long path running across the farm, and Farmer John knows that Bessie has to be at some location on this path. If we think of the path as a number line, then Farmer John is currently at position $x$ and Bessie is currently at position $y$ (unknown to Farmer John). If Farmer John knew where Bessie was located, he could walk directly to her, traveling a distance of $|x - y|$. Unfortunately, it is dark outside and Farmer John can't see anything. The only way he can find Bessie is to walk back and forth until he eventually reaches her position.

Trying to figure out the best strategy for walking back and forth in his search, Farmer John consults the computer science research literature. He is somewhat amused to find that computer scientists have studied this exact problem in the past, and that it is actually called the "Lost Cow Problem" (this is actually true!).

The recommended strategy is to move to position $x+1$, then reverse direction and move to position $x-2$, then to position $x+4$, and so on, in a "zig zag" pattern. Each step moves twice as far from his initial starting position as the step before. As he read during his study of algorithms for the lost cow problem, this approach guarantees that he will at worst travel 9 times the direct distance $|x-y|$ before he finds Bessie (this is also true, and the factor of 9 is the smallest worst case guarantee any strategy can achieve).

Farmer John wants to verify this result. Given $x$ and $y$, compute the total distance he travels under the zig-zag search strategy above until he finds Bessie. He stops the first moment he reaches position $y$.

The single line of input contains two distinct space-separated integers $x$ and $y$. Both are in the range $0$ to $1\,000$.

Print one line containing the distance Farmer John travels to reach Bessie.