10842: ABC153 - D - Caracal vs Monster
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Description
Caracal is fighting with a monster.
The health of the monster is $H$.
Caracal can attack by choosing one monster. When a monster is attacked, depending on that monster's health, the following happens:
- If the monster's health is $1$, it drops to $0$.
- If the monster's health, $X$, is greater than $1$, that monster disappears. Then, two new monsters appear, each with the health of $\lfloor X/2 \rfloor$.
($\lfloor r \rfloor$ denotes the greatest integer not exceeding $r$.)
Caracal wins when the healths of all existing monsters become $0$ or below.
Find the minimum number of attacks Caracal needs to make before winning.
The health of the monster is $H$.
Caracal can attack by choosing one monster. When a monster is attacked, depending on that monster's health, the following happens:
- If the monster's health is $1$, it drops to $0$.
- If the monster's health, $X$, is greater than $1$, that monster disappears. Then, two new monsters appear, each with the health of $\lfloor X/2 \rfloor$.
($\lfloor r \rfloor$ denotes the greatest integer not exceeding $r$.)
Caracal wins when the healths of all existing monsters become $0$ or below.
Find the minimum number of attacks Caracal needs to make before winning.
Input
Input is given from Standard Input in the following format:
```
$H$
```
```
$H$
```
Output
Find the minimum number of attacks Caracal needs to make before winning.
Constraints
- $1 \leq H \leq 10^{12}$
- All values in input are integers.
- All values in input are integers.
Sample 1 Input
2
Sample 1 Output
3
When Caracal attacks the initial monster, it disappears, and two monsters appear, each with the health of $1$.
Then, Caracal can attack each of these new monsters once and win with a total of three attacks.
Sample 2 Input
4
Sample 2 Output
7
Sample 3 Input
1000000000000
Sample 3 Output
1099511627775