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 (3.8.2) (judge verdict: Accepted)

def solve(n: int) -> int:
    mod = 1e9 + 7
    n_bin = '0' + bin(n)[2:]

    dp = [[0, 0, 0] for _ in range(len(n_bin))]
    dp[-1][0] = 1
    for i in range(len(n_bin) - 2, -1, -1):
        for s in range(3):
            for k in range(3):
                s2 = min(2, 2 * s + int(n_bin[len(n_bin) - i - 1]) - k)
                if s2 >= 0:
                    dp[i][s2] = int((dp[i][s2] + dp[i + 1][s]) % mod)

    return int(sum(dp[0]) % mod)

n = int(input())
print(solve(n))