You are given $n$ bulbs arranged in a row, numbered from $1$ to $n$. Initially, all bulbs are turned off.

Each day, exactly one bulb is switched on. You are given an array, bulbs of length $n$ where bulbs[i] $= x$ means that on day $i + 1$ (1‑indexed), the bulb at position $x$ (also 1‑indexed) is turned on.

So, given an integer k, determine the earliest day (the smallest day number) on which there are two bulbs that are on such that exactly k bulbs are off between them.

If no such day exists, return $-1$.

Constraints:

• $n ==$ bulbs.length

• $1 \leq n \leq 10^3$

• $1 \leq$ bulbs[i] $\leq n$

• bulbs is a permutationIt is a sequence that contains every integer from 1 to n exactly once and in any order. of numbers from $1$ to $n$

• $0 \leq$ k $\leq 10^3$

Let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding on how to solve this problem.

Implement your solution in the following coding playground.