TARGET = 77
results = {}              
def gameResult( x, y ):
  if (x,y) in results: return results[x,y]     
  if x + y >= TARGET: return 0
  nextCodes = [ gameResult( x+1, y ), gameResult( x*2, y ),
                gameResult( x, y+1 ), gameResult( x, y*2 ) ]
  negative = [c for c in nextCodes if c <= 0]
  if negative:
    res = -max(negative) + 1
  else:
    res = -max(nextCodes)
  results[x,y] = res                        
  return res
 
X = 7
for S in range(TARGET-X-1,0,-1):
  r = gameResult( X, S )
  print( "{:d} {:d}".format(S, r) )
# your code goes here

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