{"app":{"locale":"en-GB"},"problem":{"content":"

Let $R(M, N)$ be the number of lattice points $(x, y)$ which satisfy $M\\!\\lt\\!x\\!\\le\\!N$, $M\\!\\lt\\!y\\!\\le\\!N$ and $\\large\\left\\lfloor\\!\\frac{y^2}{x^2}\\!\\right\\rfloor$ is odd.
We can verify that $R(0, 100) = 3019$ and $R(100, 10000) = 29750422$.
Find $R(2\\cdot10^6, 10^9)$.

Note: $\\lfloor x\\rfloor$ represents the floor function.

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