Is the seed of the mersenne_twister_engine instance invariant?

Short question I couldn't find an answer to: I have two instances g1 and g2 of std::mt19937. If I seed g1 and g2 with a common int x, is it guaranteed that the sequence of samples generated by g1 is the same as the sequence of samples generated by g2 (assuming the same distributions are used, of course)? Or is this an "instance seed", i.e. is it only guaranteed that I may reproduce the sequence generated by g1 if I reseed it later on to x?