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)

MOD=10**9+7
N = int(input())
K = len(bin(N)) - 2
DP = [[0]*3 for _ in range(K+1)]
DP[0][0] = 1
for k in range(K):
    if N & (1 << K - k - 1):
        DP[k+1][0] = DP[k][0]
        DP[k+1][1] = (DP[k][0] + DP[k][1]) % MOD
        DP[k+1][2] = (DP[k][1]*2 + DP[k][2]*3) % MOD
    else:
        DP[k+1][0] = (DP[k][0] + DP[k][1]) % MOD
        DP[k+1][1] = DP[k][1]
        DP[k+1][2] = (DP[k][1] + DP[k][2]*3) % MOD
print(sum(DP[-1]) % MOD)