2350 - Shortest Impossible Sequence of Rolls\.

Hard

You are given an integer array rolls of length n and an integer k. You roll a k sided dice numbered from 1 to k, n times, where the result of the <code>i^th</code> roll is rolls[i].

Return the length of the shortest sequence of rolls that cannot be taken from rolls.

A sequence of rolls of length len is the result of rolling a k sided dice len times.

Note that the sequence taken does not have to be consecutive as long as it is in order.

Example 1:

Input: rolls = 4,2,1,2,3,3,2,4,1, k = 4

Output: 3

Explanation: Every sequence of rolls of length 1, 1, 2, 3, 4, can be taken from rolls.

Every sequence of rolls of length 2, 1, 1, 1, 2, ..., 4, 4, can be taken from rolls.

The sequence 1, 4, 2 cannot be taken from rolls, so we return 3.

Note that there are other sequences that cannot be taken from rolls.

Example 2:

Input: rolls = 1,1,2,2, k = 2

Output: 2

Explanation: Every sequence of rolls of length 1, 1, 2, can be taken from rolls.

The sequence 2, 1 cannot be taken from rolls, so we return 2.

Note that there are other sequences that cannot be taken from rolls but 2, 1 is the shortest.

Example 3:

Input: rolls = 1,1,3,2,2,2,3,3, k = 4

Output: 1

Explanation: The sequence 4 cannot be taken from rolls, so we return 1. Note that there are other sequences that cannot be taken from rolls but 4 is the shortest.

Constraints:

• n == rolls.length

• <code>1 <= n <= 10⁵</code>

• <code>1 <= rollsi<= k <= 10⁵</code>