Fox Ciel studies number theory.

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


-----Input-----

The first line contains an integer k (0 ≤ k ≤ 10^9).


-----Output-----

Print a single integer — the number of required sets modulo 1000000007 (10^9 + 7).


-----Examples-----
Input
1

Output
2

Input
2

Output
3

Input
3

Output
5

Input
4

Output
6



-----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}.

Difficulty: VERY_HARD

Solutions:
from math import factorial
MOD = 10 ** 9 + 7
k = int(input())
bink = list(map(int, bin(k)[2:]))
N = len(bink)
dp = [[[0, 0] for j in range(i + 2)] for i in range(N + 1)]
dp[0][0][1] = 1
for i in range(1, N + 1):
	for j in range(i + 1):
		dp[i][j][0] += 2 ** j * dp[i - 1][j][0]
		if j:
			dp[i][j][0] += dp[i - 1][j - 1][0]
		odd = 2 ** (j - 1) if j else 0
		even = 2 ** j - odd
		if bink[i - 1] == 1:
			dp[i][j][0] += even * dp[i - 1][j][1]
		if bink[i - 1] == 0:
			dp[i][j][1] += even * dp[i - 1][j][1]
		else:
			dp[i][j][1] += odd * dp[i - 1][j][1]
			if j:
				dp[i][j][1] += dp[i - 1][j - 1][1]
ans = sum(map(sum, dp[-1]))
print(ans % MOD)