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<br />2<br />3<br />4<br />
2<br />3<br />5<br />6<br />
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}.
暂无题解
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