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)

n=int(input())
d=dict()
def get(n):
    if(n==1):return 1
    if(n==0):return 0
    if(n in d.keys()):return d[n]
    if(n%2==0):
        d[n]=2*get(n//2)+get(n//2-1)
    else:
        d[n]=2*get(n//2)+get(n//2+1)
    d[n]%=(10**9+7)
    return d[n]
def check(u,v,n):
    for a in range(n+1):
        b=u ^ a
        if(a+b==v):
            return 1
    return 0
#for e in range(1,n):
#    ans=0
#    for i in range(e+1):
##        for j in range(e+1):
#            ans+=check(i,j,e)
#    print(ans,get(e+1))
print(get(n+1))