A young woman uses the first procedure to deduce her utility function $U(x)$ over the range $A \leq x \leq B$. She uses the normalization $U(A)=A, U(B)=B$. To check her result, she repeats the whole procedure over the range $A^{\prime} \leq x \leq B^{\prime}$, where $A0$ and $b$. Find $a$ and $b$.