B"Vivek initially has an empty array a and some integer constant m . He performs the following algorithm: Find the expected length of a . It can be shown that it can be represented as frac{P}{Q} where P and Q are coprime integers and Q neq 0 pmod{10^9+7} . Print the value of P cdot Q^{-1} pmod{10^9+7} . The first and only line contains a single integer m ( 1 <= q m <= q 100000 ). Print a single integer -- the expected length of the array a written as P cdot Q^{-1} pmod{10^9+7} . In the first example, since Vivek can choose only integers from 1 to 1 , he will have a=[1] after the first append operation, and after that quit the algorithm. Hence the length of a is always 1 , so its expected value is 1 as well. In the second example, Vivek each time will append either 1 or 2 , so after finishing the algorithm he will end up having some number of 2 's (possibly zero), and a single 1 in the end. The expected length of the list is 1 cdot frac{1}{2} + 2 cdot frac{1}{2^2} + 3 cdot frac{1}{2^3} + ldots = 2 . "...