Monte Carlo Pi Estimation

Problem

Estimate $\pi$ using Monte Carlo simulation. Generate $N$ random points uniformly in the unit square $[0, 1]^2$ and count how many fall inside the unit quarter-circle ($x^2 + y^2 \leq 1$).

$\pi \approx 4 \times \frac{\text{points inside quarter-circle}}{N}$

Use a Linear Congruential Generator (LCG) for deterministic pseudorandom numbers:

$x_{n+1} = (1103515245 \cdot x_n + 12345) \bmod 2^{31}$

Convert to uniform $[0, 1)$: $u = x / 2^{31}$. For each point, draw two consecutive values to get coordinates $(u_1, u_2)$.

Input Format

Two space-separated integers: N seed

Output Format

The estimate of $\pi$, to 4 decimal places.