Let $A,B$ be a $\gamma$-bit integer and relatively prime. $\gcd(A,B)=1$. Also, $A-B \ge 2^{\gamma -2}$
Then, by the Euclidean Algorithm, there exist integers $x$ and $y$ such that
$Ax-By = 1$. After then, what is the size of $T=|y A -x B|$? Can we find upper bound of T?