Let \(f(a, b) =\dfrac{1}{a+b}\) when \(a+b \ne 0\).

Suppose that \(x, y, z\) are distinct integers such that \(x+y +z = 2016\) and \(f(f(x, y), z) = f(x, f(y, z))\) (where both sides of the equation exist and are welldefined).

Compute \(y\).

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