3376 - Minimum Time to Break Locks I.

Medium

Bob is stuck in a dungeon and must break n locks, each requiring some amount of energy to break. The required energy for each lock is stored in an array called strength where strength[i] indicates the energy needed to break the <code>i^th</code> lock.

To break a lock, Bob uses a sword with the following characteristics:

• The initial energy of the sword is 0.

• The initial factor X by which the energy of the sword increases is 1.

• Every minute, the energy of the sword increases by the current factor X.

• To break the <code>i^th</code> lock, the energy of the sword must reach at least strength[i].

• After breaking a lock, the energy of the sword resets to 0, and the factor X increases by a given value K.

Your task is to determine the minimum time in minutes required for Bob to break all n locks and escape the dungeon.

Return the minimum time required for Bob to break all n locks.

Example 1:

Input: strength = 3,4,1, K = 1

Output: 4

Explanation:

The locks cannot be broken in less than 4 minutes; thus, the answer is 4.

Example 2:

Input: strength = 2,5,4, K = 2

Output: 5

Explanation:

The locks cannot be broken in less than 5 minutes; thus, the answer is 5.

Constraints:

• n == strength.length

• 1 <= n <= 8

• 1 <= K <= 10

• <code>1 <= strengthi<= 10⁶</code>