A9298. Fox and Perfect Sets
编程题
普及/提高-
知识点
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 $1000000007$ $(10^{9}+7)$ .
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}.
In example 4, there are 6 such sets: {0}, {0, 1}, {0, 2}, {0, 3}, {0, 4} and {0, 1, 2, 3}.