Problem:
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

Solution in Python (3.4.3) (judge verdict: Accepted)

#!/usr/bin/env python3

from copy import deepcopy

MOD = 10 ** 9 + 7
IMAX = 200
JMAX = 2

def dp(n):
    dp = [0 for j in range(JMAX + 1)]
    dp[0] = 1
    for i in reversed(range(IMAX + 1)):
        pre = deepcopy(dp)
        dp[2] += pre[1]
        dp[2] += 2 * pre[2]
        d = ((1 << i) & n) >> i
        if d:
            dp[1] += pre[0]
            dp[2] += pre[1]
        else:
            dp[0] += pre[1]
        dp = take_mod(dp)
    return sum(dp) % MOD

def take_mod(dp):
    res = [x % MOD for x in dp]
    return res

def main():
    n = int(input())
    print(dp(n))

main()