Xor Sum

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.

Examples

Input

3

Output

5

Input

1422

Output

52277

Input

1000000000000000000

Output

787014179

inputFormat

Input

The input is given from Standard Input in the following format:

N

outputFormat

Output

Print the number of the possible pairs of integers u and v, modulo 10^9+7.

Examples

Input

3

Output

5

Input

1422

Output

52277

Input

1000000000000000000

Output

787014179

样例

3

5