##### Question Implement a "valid" 1-D convolution function in the cross-correlation sense. Given an input array of numbers, a kernel (filter) array of numbers, and a scalar bias, compute the output only at positions where the kernel **fully overlaps** the input (no padding, stride = 1), adding the bias to every output value. Concretely, for an input of length `n` and a kernel of length `k` (with `k <= n`), produce an output of length `n - k + 1` where: ``` output[i] = ( sum_{j=0}^{k-1} input[i + j] * kernel[j] ) + bias ``` 1. **Define the function signature** and clearly state your assumptions (e.g., stride = 1, no padding). 2. **Use cross-correlation semantics** — do **not** reverse the kernel before sliding it (this differs from textbook mathematical convolution, which flips the kernel). 3. **Apply the scalar bias** to each computed output element. 4. **Handle edge cases**: an empty kernel, a kernel longer than the input, and floating-point input/kernel/bias values. 5. **Analyze the time and space complexity** of your implementation.