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Problem B
Baby Panda

/problems/babypanda/file/statement/en/img-0001.jpg
a sneezing baby panda

Alex is taking care of a baby panda who seems to be unusually sniffly. Every day, the baby panda may sneeze out zero or one slime(s) into its enclosure; every night, all slimes present in the enclosure split, so that the number of slimes doubles overnight. Alex places the baby panda into a clean enclosure with $0$ slimes at the beginning of day $1$ and observes that at the end of night $n$, there are $m$ slimes in the baby panda’s enclosure. She is worried about the baby panda and wants to know the number of times the baby panda sneezed out a slime over these $n$ days.

Input

The only line of input contains the space-separated integers $n, m$ ($1 \leq n \leq 10^{18}$, $0 \leq m \leq 10^{18}$, $m$ is even), where $n$ is the number of days and $m$ is the number of slimes present after night $n$.

Output

On a single line, output the number of times that the baby panda sneezed out a slime.

Sample Input 1 Sample Output 1
10 10
2
Sample Input 2 Sample Output 2
10 128
1
Sample Input 3 Sample Output 3
13 500
6
Sample Input 4 Sample Output 4
1000000000000000000 576460752303423488
1
CPU Time limit 1 second
Memory limit 1024 MB
Author
Jacob Zhang
Source CodeSprint LA 2021
License Creative Commons License (cc by-sa)

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