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 ith lock.
To break a lock, Bob uses a sword with the following characteristics:
\n\nx by which the energy of the sword increases is 1.x.ith lock, the energy of the sword must reach at least strength[i].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.
\n
Example 1:
\n\nInput: strength = [3,4,1], k = 1
\n\nOutput: 4
\n\nExplanation:
\n\n| Time | \n\t\t\tEnergy | \n\t\t\tx | \n\t\t\tAction | \n\t\t\tUpdated x | \n\t\t
|---|---|---|---|---|
| 0 | \n\t\t\t0 | \n\t\t\t1 | \n\t\t\tNothing | \n\t\t\t1 | \n\t\t
| 1 | \n\t\t\t1 | \n\t\t\t1 | \n\t\t\tBreak 3rd Lock | \n\t\t\t2 | \n\t\t
| 2 | \n\t\t\t2 | \n\t\t\t2 | \n\t\t\tNothing | \n\t\t\t2 | \n\t\t
| 3 | \n\t\t\t4 | \n\t\t\t2 | \n\t\t\tBreak 2nd Lock | \n\t\t\t3 | \n\t\t
| 4 | \n\t\t\t3 | \n\t\t\t3 | \n\t\t\tBreak 1st Lock | \n\t\t\t3 | \n\t\t
The locks cannot be broken in less than 4 minutes; thus, the answer is 4.
\nExample 2:
\n\nInput: strength = [2,5,4], k = 2
\n\nOutput: 5
\n\nExplanation:
\n\n| Time | \n\t\t\tEnergy | \n\t\t\tx | \n\t\t\tAction | \n\t\t\tUpdated x | \n\t\t
|---|---|---|---|---|
| 0 | \n\t\t\t0 | \n\t\t\t1 | \n\t\t\tNothing | \n\t\t\t1 | \n\t\t
| 1 | \n\t\t\t1 | \n\t\t\t1 | \n\t\t\tNothing | \n\t\t\t1 | \n\t\t
| 2 | \n\t\t\t2 | \n\t\t\t1 | \n\t\t\tBreak 1st Lock | \n\t\t\t3 | \n\t\t
| 3 | \n\t\t\t3 | \n\t\t\t3 | \n\t\t\tNothing | \n\t\t\t3 | \n\t\t
| 4 | \n\t\t\t6 | \n\t\t\t3 | \n\t\t\tBreak 2nd Lock | \n\t\t\t5 | \n\t\t
| 5 | \n\t\t\t5 | \n\t\t\t5 | \n\t\t\tBreak 3rd Lock | \n\t\t\t7 | \n\t\t
The locks cannot be broken in less than 5 minutes; thus, the answer is 5.
\n\n
Constraints:
\n\nn == strength.length1 <= n <= 81 <= K <= 101 <= strength[i] <= 106n! permutation ways of breaking the locks."
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