'''
Verifier for answers for the PPCG question Finding Collatz-like rules with many loops
Input is expected from standard input as space-separated integers `d m i min_value_1 min_value_2 ...`.
E.g. for d=3 m=7 i=8 min_values=[1 2 4] the input should be "3 7 8 1 4 2"
'''
def itOne(n,d,m,i):
return (n*m+i) if n%d else n//d
def checkMin(n,d,m,i):
ni=n
while True:
ni=itOne(ni,d,m,i)
if ni<n:
return False
if ni==n:
return True
strin=input()
d,m,i,*mins=map(int,strin.split())
ok=True
minset=set()
for mine in mins:
if mine in minset or not checkMin(mine,d,m,i):
ok=False
break
minset.add(mine)
if ok:
print('d=',d,' m=',m,' i=',i,' is VERIFIED for a score of ',len(minset),'.',sep='')
else:
print('The given input FAILED the test.')
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