#K95862. Maximum Level Determination
Maximum Level Determination
Maximum Level Determination
You are given a non-negative integer x representing the total XP (experience points) a player has accumulated. The player starts at level 1. To advance from level \(L-1\) to level \(L\) for \(L \geq 2\), the required XP is \(2^{L-2}\). In other words, the total XP needed to reach level \(L\) is
\[ S(L) = \sum_{i=2}^{L} 2^{i-2} \leq x \]
Your task is to determine the maximum level a player can reach given the total XP \(x\). Note that if x is exactly equal to the boundary requirement for a level up, the player will be at the previous level.
Example:
- If
x = 0
, the player remains at level1
. - If
x = 1
, the player can reach level2
since \(2^0 = 1\). - If
x = 2
, the player only manages level2
(not enough XP for level 3).
inputFormat
The input is read from standard input (stdin) and consists of a single non-negative integer x representing the total XP.
outputFormat
Output to standard output (stdout) a single integer representing the maximum level the player can achieve with the given XP.
## sample0
1