Optimization & Lagrange Multipliers · Easy problem

The maximum of $f(x,y) = x + y$ on the circle $x^2 + y^2 = 2$ occurs at $(1, 1)$. Find the Lagrange multiplier $\lambda$ at this point, using the equation $\nabla f = \lambda \nabla g$ with $g(x,y) = x^2 + y^2$.