Let \(\vec F\) be a vector \(\vec F\left( {x,y,z} \right) = - y\hat i + 2xy\hat j + {z^3}\hat k\), for (x, y, z) ∊ R³. If C is the curve of intersection of the surfaces \({x^2} + {y^2} = 1\) and \(y + z = 2\), then the value of \(\mathop \smallint \limits_C \vec F.d\vec r\) is