Fox and Perfect Sets

1000ms

262144K

Description:

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).

Input:

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

Output:

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

Sample Input:

Sample Output:

Sample Input:

Sample Output:

Sample Input:

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Sample Input:

Sample Output:

Note:

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}.

Informação

Provedor Codeforces

Código CF388D