Task

Implement a two-step pipeline: first standardize the features by subtracting the training mean and dividing by the training standard deviation (set std to 1 where it is 0), then fit ridge regression on the standardized training data using the closed-form solution w = (Xs^T Xs + λI)^{-1} Xs^T y. Apply the same standardization to the test set and predict ytest = Xtests * w. This mimics scikit-learn's Pipeline([StandardScaler, Ridge]).

Input

• Line 1: n_train d lam — number of training samples, number of features, regularization strength λ
• Lines 2 to n_train+1: x_1 ... x_d y — training feature values followed by the target
• Line n_train+2: n_test — number of test samples
• Lines ntrain+3 to ntrain+n_test+2: x_1 ... x_d — test feature values

Output

Print the predicted values for the test samples space-separated on one line, with up to 10 significant digits each.

Example

Input:

5 2 1.0
1 2 5
2 3 8
3 4 11
4 5 14
5 6 17
3
2 3
4 5
1 1

Output:

-2.727272727 2.727272727 -6.818181818

Scaffolding

Submit a Python file defining:

def sklearn_pipeline(X_train: list[list[float]], y_train: list[float],
                     X_test: list[list[float]], lam: float) -> list[float]:
    ...

Receives training features and targets, test features, and a regularization strength; returns the predicted values for the test set after applying feature standardization and ridge regression.