## Pencils of rays

### Problem 372

Published on Saturday, 18th February 2012, 01:00 pm; Solved by 267; Difficulty rating: 60%
Let R(`M`, `N`) be the number of lattice points (`x`, `y`) which satisfy `M`<`x`≤`N`, `M`<`y`≤`N` and is odd.

We can verify that R(0, 100) = 3019 and R(100, 10000) = 29750422.

Find R(2·10^{6}, 10^{9}).

__ Note__: represents the floor function.