Welcome to the China Collegiate Programming Contest (CCPC) Zhengzhou onsite! Bobo has noticed that the initials of "Zheng" and "Zhou" are both Z. This motivates him to study the well-known Z-order curve.

To introduce the Z-order curve, we first introduce the Moser–de Bruijn sequence $$$(B_t)_{t \ge 0}$$$, the ordered sequence of numbers whose binary representation has nonzero digits only in the even positions. The first few terms of the Moser-de Bruijn sequence are $$$0, 1, 4, 5, 16, 17, 20, 21$$$.

Each non-negative integer $$$z$$$ can be uniquely decomposed into the sum of $$$B_x$$$ and $$$2B_y$$$. Therefore, we can write down all natural numbers in an infinitely large table. The Z-order curve is then obtained by connecting all the numbers in numerical order.

Illustration of Z-curve

Bobo now challenges you with the following problem: For a given fragment extracted from the Z-curve from $$$L$$$ to $$$R$$$, find the smallest integer $$$l$$$ such that the Z-curve from $$$l$$$ to $$$l+R-L$$$ is identical to the given fragment (i.e., the curve from $$$l$$$ to $$$l+R-L$$$ can be obtained by translating the curve from $$$L$$$ to $$$R$$$).

Please note that in this problem, the curve is directed. Specifically, the curve from $$$1$$$ to $$$2$$$ is NOT identical to the curve from $$$3$$$ to $$$4$$$.