elapsed | Children ---|--- `0` | `[_0_ , 1, 2, 3]` `1` | `[0, _1_ , 2, 3]` `2` | `[0, 1, _2_ , 3]`

Constraints

2 <= n <= 50
1 <= k <= 50

Note: This question is the same as 2582: Pass the Pillow.

Solution

Method 1 – Simulation with Modulo Arithmetic

Intuition

The ball moves back and forth between the ends. The movement forms a cycle of length 2 * (n - 1). We can use modulo arithmetic to find the position after k seconds efficiently.

Approach

Compute the cycle length as 2 * (n - 1).
The effective time is k % cycle.
If the effective time is less than n, the ball is moving right, so the answer is effective time.
Otherwise, the ball is moving left, so the answer is

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