Using solve_S_unit_equation for integers

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Hi, I would like to use the routine solve_S_unit_equation to find all integers A,B with A-B=1,2 generated by a set primes. For instance the input set {2,31} should return [(2, 1), (4, 2), (32, 31), (64, 62)]. The input set {2,3,11} should return [(2, 1), (3, 1), (3, 2), (4, 2), (4, 3), (6, 4), (8, 6), (9, 8), (11, 9), (12, 11), (18, 16), (24, 22), (33, 32), (66, 64), (243, 242), (486, 484)]. The problem I encounter is that the routine is based on defining a field, but ZZ does not work. Thanks in advance for the solution!