Convolution is an important component in Convolutional Neural Networks $($CNN$).$ As shown in the following figure, a convolutional later in CNN can be implemented with matrix multiplication. It is also assumed that the convolution filters have been converted to a matrix W with width W$\_$w and with height Wh$,$ and all input features have been converted to matrix X with width X$\_$w and with height X$\_$h$.$

Part $1$: Write a serial C code to calculate the output feature Y if it is implemented with matrix multiplication

Part $2$: If implementing the convolution calculation $($using matrix multiplication$)$ in parallel with CUDA, explain how to divide the problem into subtasks and how to assign multiple threads to these subtasks using a ID thread organization.

Part $3$: Write a CUDA kernel function to calculate output feature Y based on parallel algorithm in Part $2.$