Prove that the following two problems have the same complexity
by giving a lineartime reductions between the two.
3SUM: given n
integers x_{1}, ..., x_{n}, are there
three distinct integers i, j, and k such that
x_{i} + x_{j} + x_{k} = 0.
3SUMPLUS: given n
integers x_{1}, ..., x_{n},
and an integer b are there
three distinct integers i, j, and k such that
x_{i} + x_{j} + x_{k} = b.

Give a lineartime reduction from 3SUM to 3SUMPLUS.
To demonstrate your reduction, give the 3SUMPLUS instance that
you would construct to solve the following 3SUM instance:
x_{1}, ..., x_{n}.

Give a lineartime reduction from 3SUMPLUS to 3SUM.
To demonstrate your reduction, give the 3SUM instance that
you would construct to solve the following 3SUMPLUS instance:
b, x_{1}, ..., x_{n}.