Need Help Reducing Subset Sum to Show a Problem is NP-Complete
Here are some hints:


Focus on the case $d = 1$.
Given a target $T$ in SUBSET-SUM, we can change it to a target $T'$ by adding the number $T' - T$; this should work if $T'$ is sufficiently large.
Given a SUBSET-SUM without constraints on the size of the subset, we can get an equivalent problem with such a constraint by adding a suitable number of zeroes to the (multi)set.


If we insist on a set, we need to do more cunning in 3.