You are given two integer arrays, skill and mana, of length n and m, respectively.

In a laboratory, n wizards must brew m potions in order. Each potion has a mana capacity mana[j] and must pass through all the wizards sequentially to be brewed properly. The time taken by the ith wizard on the jth potion is timeij = skill[i] * mana[j].

Since the brewing process is delicate, a potion must be passed to the next wizard immediately after the current wizard completes their work. This means the timing must be synchronized so that each wizard begins working on a potion exactly when it arrives.

Return the minimum amount of time required for the potions to be brewed properly.

 

Example 1:

Input: skill = [1,5,2,4], mana = [5,1,4,2]

Output: 110

Explanation:

Potion Number Start time Wizard 0 done by Wizard 1 done by Wizard 2 done by Wizard 3 done by
0 0 5 30 40 60
1 52 53 58 60 64
2 54 58 78 86 102
3 86 88 98 102 110

As an example for why wizard 0 cannot start working on the 1st potion before time t = 52, consider the case where the wizards started preparing the 1st potion at time t = 50. At time t = 58, wizard 2 is done with the 1st potion, but wizard 3 will still be working on the 0th potion till time t = 60.

Example 2:

Input: skill = [1,1,1], mana = [1,1,1]

Output: 5

Explanation:

  1. Preparation of the 0th potion begins at time t = 0, and is completed by time t = 3.
  2. Preparation of the 1st potion begins at time t = 1, and is completed by time t = 4.
  3. Preparation of the 2nd potion begins at time t = 2, and is completed by time t = 5.

Example 3:

Input: skill = [1,2,3,4], mana = [1,2]

Output: 21

 

Constraints: