C - Counting ones

Time limit: 2 s
Memory limit: 256 MiB
Languages: C, C++, Java, Haskell, ... (details)

Carl is right now the happiest child in the world: he has just learned this morning what the binary system is. He learned, for instance, that the binary representation of a positive integer $k$ is a string $a_na_{n-1}...a_1a_0$ where each $a_i$ is a binary digit $0$ or $1$, starting with $a_n= 1$, and such that $k =\sum_{i=0}^{n}a_i \times 2^i$. It is really nice to see him turning decimal numbers into binary numbers, and then adding and even multiplying them.

Caesar is Carl's older brother, and he just can't stand to see his little brother so happy. So he has prepared a challenge: "Look Carl, I have an easy question for you: I will give you two integers $A$ and $B$, and you have to tell me how many $1$'s there are in the binary representation of all the integers from $A$ to $B$, inclusive. Get ready". Carl agreed to the challenge. After a few minutes, he came back with a list of the binary representation of all the integers from $1$ to $100$. "Caesar, I'm ready". Caesar smiled and said: "Well, let me see, I choose $A = 10^{15}$ and $B = 10^{16}$. Your list will not be useful".

Carl hates losing to his brother so he needs a better solution fast. Can you help him?

Input

A single line that contains two integers $A$ and $B$ $(1 \leq A \leq B \leq 10^{16})$.

Output

Output a line with an integer representing the total number of digits $1$ in the binary representation of all the integers from $A$ to $B$, inclusive.

Sample test(s)

Input
9007199254740992 9007199254740992
Output
1
Input
1000000000000000 10000000000000000
Output
239502115812196372
Input
2 12
Output
21