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CodeForces 388D Fox and Perfec

[编程题]CodeForces 388D Fox and Perfec

时间限制：C/C++ 1秒，其他语言2秒空间限制：C/C++ 256M，其他语言512M
算法知识视频讲解

Fox Ciel studies number theory.

She thinks a non-empty set S contains non-negative integers is perfect if and only if for any $\text{[math]}$ ( a can be equal to b ), $\text{[math]}$ . 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 (10⁹ + 7).

输入描述:

The first line contains an integer k (0 ≤ k ≤ 10⁹).

输出描述:

Print a single integer — the number of required sets modulo 1000000007(10⁹ + 7).

示例1

输入

1<br />2<br />3<br />4<br />

输出

2<br />3<br />5<br />6<br />

备注:

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}.

算法知识视频讲解