Given positive integers $b, c, d, x, y$ such that: $\frac{a}{b}>\frac{x}{y}>\frac{c}{d}$ and $ad-bc=1$ prove that $x\ge a+c$ and $y\ge b+d$
How prove that $q \geq b+d$ for $ad-bc = 1$ and $\frac{a}{b} > \frac{p}{q} > \frac{c}{d}$?