Let's define a simple recursive function F(n), where

   Let's define the function S(p, q) as follows:

   In this problem you have to calculate S(p, q) on given values of p and q.

Input

First line contains two nonnegative integers p and q (0≤p ≤ q≤2∙10⁹), separated by space.

Output      

Print the value S(p, q) on first line.

Samples