Rock Climbing

A rock wall has n holds. Each hold is represented by coordinates (x, y). From the current position (x, y), you may move to another hold (a, b) only if |a - x| <= 2 and |b - y| <= 2.

You start at (0, 0). Using the holds, you want to reach the top of the wall, whose height is y = T. The x-coordinate at the top does not matter. Find the minimum number of moves needed to reach that height.

The first line contains the number of holds n and the target height T. (1 <= n <= 50,000, 1 <= T <= 200,000)

Each of the next n lines contains the coordinates x, y of one hold. Both coordinates are at least 0, and they satisfy x <= 1,000,000 and y <= T. The starting position (0, 0) is not included in the input.

Print the minimum number of moves needed to reach the top. If the top cannot be reached, print -1.