Score : 600 points
You are given a positive integer N. Find the number of the pairs of integers u and v (0≦u,v≦N) such that there exist two non-negative integers a and b satisfying a xor b=u and a+b=v. Here, xor denotes the bitwise exclusive OR. Since it can be extremely large, compute the answer modulo 10^9+7.
The input is given from Standard Input in the following format:
N
Print the number of the possible pairs of integers u and v, modulo 10^9+7.
3
5
The five possible pairs of u and v are:
u=0,v=0 (Let a=0,b=0, then 0 xor 0=0, 0+0=0.)
u=0,v=2 (Let a=1,b=1, then 1 xor 1=0, 1+1=2.)
u=1,v=1 (Let a=1,b=0, then 1 xor 0=1, 1+0=1.)
u=2,v=2 (Let a=2,b=0, then 2 xor 0=2, 2+0=2.)
u=3,v=3 (Let a=3,b=0, then 3 xor 0=3, 3+0=3.)
1422
52277
1000000000000000000
787014179