Task

Given predictions from an ensemble of k models at a single test point, compute the classical bias-variance decomposition of expected squared error. The mean prediction is meanpred = (1/k) * sum(preds). Bias squared = (meanpred - ytrue)². Variance = (1/k) * sum((p - meanpred)²). Irreducible error = sigma², the noise variance. Total expected error = bias_squared + variance + irreducible.

Input

• Line 1: k sigma2 — number of model predictions, noise variance σ²
• Line 2: p_1 p_2 ... p_k — predictions from each model, space-separated
• Line 3: y_true — the true target value

Output

Print four values each on its own line: bias_squared, variance, irreducible, total — each with up to 10 significant digits.

Example

Input:

5 0.25
2.0 2.5 3.0 2.8 2.2
3.0

Output:

0.25
0.136
0.25
0.636

Scaffolding

Submit a Python file defining:

def bias_variance_decomp(preds: list[float], y_true: float,
                         sigma2: float) -> tuple[float, float, float, float]:
    ...

Receives a list of model predictions, the true target value, and the noise variance; returns a tuple (bias_squared, variance, irreducible, total).