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 C (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <stdlib.h>
#define ll long long
#define rep(i,l,r)for(ll i=(l);i<(r);i++)
#define bit(n,m)((n>>m)&1)

#define M 1000000007
//a^b=x,a+b=y,a|b=bとして(a,b)と(x,y)が1対1対応するので(a,b)の個数を数えれば良い
//dp[見た桁数][a^bが(n mod 2**keta)以下か][a+b>=2**ketaか][(a+b mod 2**keta)が(n mod 2**keta)以下か]
ll dp[99][2][2][2];
int main(){
	ll n;
	scanf("%lld",&n);
	dp[0][1][0][1]=1;
	rep(keta,0,62){
		rep(p,0,2)rep(q,0,2)rep(r,0,2){
			//0a,0bのとき0x,(0+繰り上がり)y
			dp[keta+1][p||bit(n,keta)][0][(q^r)?r:bit(n,keta)]+=dp[keta][p][q][r];
			//0a,1bのとき1x,(1+繰り上がり)y
			dp[keta+1][p&&bit(n,keta)][q][(q^r)?bit(n,keta):r]+=dp[keta][p][q][r];
			//1a,1bのとき0x,1(繰り上がり)y
			dp[keta+1][p||bit(n,keta)][1][(q^r)?r:bit(n,keta)]+=dp[keta][p][q][r];
		}
		rep(p,0,2)rep(q,0,2)rep(r,0,2)dp[keta+1][p][q][r]%=M;
	}
	printf("%lld\n",dp[62][1][0][1]);
	return 0;
}