Implement Self-Attention (Single-Head)

Problem: Implement Self-Attention (Single-Head) Implement scaled dot-product self-attention (single head) in a Transformer. Given: sequence length n dimension d real matrices Q, K, V of shape n x d optional attention mask M of shape n x n: M[i][j] = 0 means allowed M[i][j] = 1 means disallowed (set the corresponding logit to -inf before softmax) Compute: S = (Q * K^T) / sqrt(d) If mask is provided, set S[i][j] = -inf wherever M[i][j] = 1 A = softmax(S) applied row-wise Output O = A * V with shape n x d Input (stdin) First line: two integers n d Next n lines: matrix Q Next n lines: matrix K Next n lines: matrix V Next line: integer has_mask (0 or 1) If has_mask = 1, next n lines: matrix M (0/1) Output (stdout) Print O as n lines, each with d floats rounded to 6 decimals. Constraints 1 <= n <= 50 1 <= d <= 50 absolute value of inputs <= 10 Example Input: 2 2 1 0 0 1 1 0 0 1 1 2 3 4 0 Output: 1.660476 2.660476 2.339524 3.339524 Example Input 1 1 1 1 2 0 Output 2.000000