3154 - Find Number of Ways to Reach the K-th Stair.

Hard

You are given a non-negative integer k. There exists a staircase with an infinite number of stairs, with the lowest stair numbered 0.

Alice has an integer jump, with an initial value of 0. She starts on stair 1 and wants to reach stair k using any number of operations. If she is on stair i, in one operation she can:

• Go down to stair i - 1. This operation cannot be used consecutively or on stair 0.

• Go up to stair <code>i + 2^jump</code>. And then, jump becomes jump + 1.

Return the total number of ways Alice can reach stair k.

Note that it is possible that Alice reaches the stair k, and performs some operations to reach the stair k again.

Example 1:

Input: k = 0

Output: 2

Explanation:

The 2 possible ways of reaching stair 0 are:

• Alice starts at stair 1.

• Alice starts at stair 1.

Example 2:

Input: k = 1

Output: 4

Explanation:

The 4 possible ways of reaching stair 1 are:

• Alice starts at stair 1. Alice is at stair 1.

• Alice starts at stair 1.

• Alice starts at stair 1.

• Alice starts at stair 1.

Constraints:

• <code>0 <= k <= 10⁹</code>