200661: [AtCoder]ARC066 D - Xor Sum
Description
Score : $600$ points
Problem Statement
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 $10^9+7$.
Constraints
- $1≦N≦10^{18}$
Input
The input is given from Standard Input in the following format:
$N$
Output
Print the number of the possible pairs of integers $u$ and $v$, modulo $10^9+7$.
Sample Input 1
3
Sample Output 1
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 $3$ $xor$ $0=3$, $3+0=3$.）
Sample Input 2
1422
Sample Output 2
52277
Sample Input 3
1000000000000000000
Sample Output 3
787014179