THE CONVOLUTION OUTPUT SHAPE

Difficulty: Medium Tags: Deep Learning, CNNs, Tensor Shapes

Story

A vision pipeline allocates output tensors for a convolution. A shape calculation that ignores stride and padding causes buffer overruns. Compute the output height and width for a 2D convolution with symmetric padding.

The Math

For input dimension I, kernel K, padding P, and stride S:

O = floor((I + 2P - K) / S) + 1

Apply independently to height and width. The input guarantees positive output dimensions.

Input Format

H, W, K, P, S.

Output Format

Output height and output width, as integers.

Constraints

• 1 <= H, W <= 10^6, 1 <= K, S <= 10^5, 0 <= P <= 10^5.
• Time limit: 1.0 second.

Example

Input

H=32, W=32, K=3, P=1, S=2

Output

16 16

Explanation: floor((32 + 2 - 3) / 2) + 1 = 16 in both dimensions.