JavaScript, 112 bytes
k=>x=>(r=Array(k).fill(''),[...`${x<0?2*~x+1:2*x}`].map((c,i,s)=>r[(s.length-i)%k]+=c),r.map(v=>v&1?~(v/2):v/2))
- convert to non-negative
- (n*k+i)th digit to i-th number
- convert back
tsh
- 35.6k
- 2
- 34
- 129