GCD and subsequence Help

I recently encountered this problem on hackerearth. can anybody help me on this?


Given an array of size N and an integer K. Find

Sum of subsequence \times GCD of subsequence over all K length subsequences. Print it modulo 998244353

1 \leq K \leq N \leq 3 \times 10^4

A[i] \leq 5 \times 10^4

For more details refer the image link provided.

The problem was from a hiring challenge so it is not visible now(challenge ended on 3rd Aug).