CF388D.Fox and Perfect Sets

普及/提高-

通过率：0%

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题目描述

Fox Ciel studies number theory.

She thinks a non-empty set $S$ contains non-negative integers is perfect if and only if for any ( $a$ can be equal to $b$ ), . Where operation $xor$ means exclusive or operation (http://en.wikipedia.org/wiki/Exclusive_or).

Please calculate the number of perfect sets consisting of integers not greater than $k$ . The answer can be very large, so print it modulo $1000000007$ $(10^{9}+7)$ .

输入格式

The first line contains an integer $k$ ( $0<=k<=10^{9}$ ).

输出格式

Print a single integer — the number of required sets modulo $1000000007$ $(10^{9}+7)$ .

输入输出样例

输入#1
```
1
```
输出#1
```
2
```
输入#2
```
2
```
输出#2
```
3
```
输入#3
```
3
```
输出#3
```
5
```
输入#4
```
4
```
输出#4
```
6
```

说明/提示

In example 1, there are 2 such sets: {0} and {0, 1}. Note that {1} is not a perfect set since 1 xor 1 = 0 and {1} doesn't contain zero.

In example 4, there are 6 such sets: {0}, {0, 1}, {0, 2}, {0, 3}, {0, 4} and {0, 1, 2, 3}.

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