Fox and Perfect Sets
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 (109+7).
The first line contains an integer k (0≤k≤109).
Print a single integer − the number of required sets modulo 1000000007 (109+7).
1
2
2
3
3
5
4
6
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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