Shortest Path on a Triangular Grid

There is a triangular grid made of small equilateral triangles. The top row contains one triangle numbered 1. For row r, there are 2r - 1 triangles, numbered consecutively from left to right. Therefore, the last number in row r is r^2.

You want to move from the triangle numbered A to the triangle numbered B. In one move, you may move only to a neighboring triangle that shares an edge with the current triangle. You cannot move through a vertex, and you cannot move outside the triangular grid.

The length of a path is the number of edges crossed along the way. Given A and B, find the minimum possible path length.

The first line contains two integers A and B. (1 ≤ A, B ≤ 1,000,000,000)

Print the length of the shortest path.