Sum of Total Strength of Wizards
As the ruler of a kingdom, you have an army of wizards at your command.
You are given a 0-indexed integer array strength, where strength[i] denotes the strength of the i^th wizard. For a contiguous group of wizards (i.e. the wizards' strengths form a subarray of strength), the total strength is defined as the product of the following two values:
- The strength of the weakest wizard in the group.
- The total of all the individual strengths of the wizards in the group.
Return the sum of the total strengths of all contiguous groups of wizards. Since the answer may be very large, return it modulo 10^9 + 7.
A subarray is a contiguous non-empty sequence of elements within an array.
Example 1
Input
strength = [1,3,1,2]Output
44The sum of the total strengths of all contiguous groups is 1 + 9 + 1 + 4 + 4 + 4 + 3 + 5 + 6 + 7 = 44.
Example 2
Input
strength = [5,4,6]Output
213The sum of the total strengths of all contiguous groups is 25 + 16 + 36 + 36 + 40 + 60 = 213.
Constraints
- 1 <= strength.length <= 10^5
- 1 <= strength[i] <= 10^9