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 i^th 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 i^th 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:

Time	Energy	x	Action	Updated x
0	0	1	Nothing	1
1	1	1	Break 3^rd Lock	2
2	2	2	Nothing	2
3	4	2	Break 2^nd Lock	3
4	3	3	Break 1^st Lock	3

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:

Time	Energy	x	Action	Updated x
0	0	1	Nothing	1
1	1	1	Nothing	1
2	2	1	Break 1^st Lock	3
3	3	3	Nothing	3
4	6	3	Break 2ⁿ^d Lock	5
5	5	5	Break 3^r^d Lock	7

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
1 <= strength[i] <= 10⁶