Real numbers \( x \), \( y \), and \( z \) satisfy the inequalities \( 0<x<1 \), \( -1<y<0 \), and \( 1<z<2 \). Among the following expressions, find the one that is necessarily positive: \( y + x^2 \), \( y + xz \), \( y + y^2 \), \( y + 2y^2 \), \( y + z \). The original answer is in the form \( a \cdot y + b \cdot z \), where \( a \) and \( b \) are non-zero integers. Please find the value of \( a + b \).

Let's think step by step and output the final answer within \boxed{}.
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