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# 1589. Maximum Sum Obtained of Any Permutation

<https://leetcode.com/problems/maximum-sum-obtained-of-any-permutation>

## Description

We have an array of integers, `nums`, and an array of `requests` where `requests[i] = [starti, endi]`. The `ith` request asks for the sum of `nums[starti] + nums[starti + 1] + ... + nums[endi - 1] + nums[endi]`. Both `starti` and `endi` are *0-indexed*.

Return *the maximum total sum of all requests **among all permutations** of* `nums`.

Since the answer may be too large, return it **modulo** `109 + 7`.

**Example 1:**

```
**Input:** nums = [1,2,3,4,5], requests = [[1,3],[0,1]]
**Output:** 19
**Explanation:** One permutation of nums is [2,1,3,4,5] with the following result: 
requests[0] -> nums[1] + nums[2] + nums[3] = 1 + 3 + 4 = 8
requests[1] -> nums[0] + nums[1] = 2 + 1 = 3
Total sum: 8 + 3 = 11.
A permutation with a higher total sum is [3,5,4,2,1] with the following result:
requests[0] -> nums[1] + nums[2] + nums[3] = 5 + 4 + 2 = 11
requests[1] -> nums[0] + nums[1] = 3 + 5  = 8
Total sum: 11 + 8 = 19, which is the best that you can do.
```

**Example 2:**

```
**Input:** nums = [1,2,3,4,5,6], requests = [[0,1]]
**Output:** 11
**Explanation:** A permutation with the max total sum is [6,5,4,3,2,1] with request sums [11].
```

**Example 3:**

```
**Input:** nums = [1,2,3,4,5,10], requests = [[0,2],[1,3],[1,1]]
**Output:** 47
**Explanation:** A permutation with the max total sum is [4,10,5,3,2,1] with request sums [19,18,10].
```

**Constraints:**

* `n == nums.length`
* `1 <= n <= 105`
* `0 <= nums[i] <= 105`
* `1 <= requests.length <= 105`
* `requests[i].length == 2`
* `0 <= starti <= endi < n`

## ac

```java
```