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 PHP (5.6.30) (judge verdict: Time Limit Exceeded)

<?php
    $n = fgets(STDIN);
    $count = 0;
    $check = array();
    for($sum=0;$sum<=$n;$sum++){
        for($i=0;$i<=floor($sum/2);$i++){
    //        echo "sum:",$sum," a:",$i," b:",$sum-$i;
     //       echo PHP_EOL;
            $a = $i;
            $b = $sum - $a;
            $xor = $a ^ $b;
            if(($xor <= $n || $a == $b) && ($check[$sum][$xor] == 0 )){
 //               echo "xor:",$a ^ $b," a:",$a," b:","$b"; 
   //    echo PHP_EOL;
  //              echo PHP_EOL;
                $count++;
                if($count == 1000000007){
                    $count = 0;
                }
                $check[$sum][$xor] = 1;
            }
        }
    }
    echo $count;

 
?>