--- Day 13: A Maze of Twisty Little Cubicles ---

You arrive at the first floor of this new building to discover a much less welcoming environment than the shiny atrium of the last one. Instead, you are in a maze of twisty little cubicles, all alike.

Every location in this area is addressed by a pair of non-negative integers (x,y). Each such coordinate is either a wall or an open space. You can't move diagonally. The cube maze starts at 0,0 and seems to extend infinitely toward positive x and y; negative values are invalid, as they represent a location outside the building. You are in a small waiting area at 1,1.

While it seems chaotic, a nearby morale-boosting poster explains, the layout is actually quite logical. You can determine whether a given x,y coordinate will be a wall or an open space using a simple system:

• Find x*x + 3*x + 2*x*y + y + y*y.
• Add the office designer's favorite number (your puzzle input).
• Find the binary representation of that sum; count the number of bits that are 1.
  • If the number of bits that are 1 is even, it's an open space.
  • If the number of bits that are 1 is odd, it's a wall.

For example, if the office designer's favorite number were 10, drawing walls as # and open spaces as ., the corner of the building containing 0,0 would look like this:

  0123456789
0 .#.####.##
1 ..#..#...#
2 #....##...
3 ###.#.###.
4 .##..#..#.
5 ..##....#.
6 #...##.###

Now, suppose you wanted to reach 7,4. The shortest route you could take is marked as O:

  0123456789
0 .#.####.##
1 .O#..#...#
2 #OOO.##...
3 ###O#.###.
4 .##OO#OO#.
5 ..##OOO.#.
6 #...##.###

Thus, reaching 7,4 would take a minimum of 11 steps (starting from your current location, 1,1).

What is the fewest number of steps required for you to reach 31,39?