# Permute List to Make Largest Range Sum

You are given a list of integers `nums`

and a two-dimensional list of integers `ranges`

. Each element in `ranges`

contains `[i, j]`

, meaning to sum the numbers in `nums`

between `i`

to `j`

inclusive.

Given that you can first permute `nums`

in any order, return the maximum possible total of all range sums. Return the result mod `10 ** 9 + 7`

.

**Constraints**

`0 ≤ n ≤ 100,000`

where`n`

is the length of`nums`

`0 ≤ m ≤ 100,000`

where`m`

is the length of`ranges`

https://binarysearch.com/problems/Permute-List-to-Make-Largest-Range-Sum

## Examples

### Example 1

**Input**

- nums =
`[1, 2, 3, 4, 5, 6]`

- ranges =

```
[[0,1],
[1,3]]
```

**Output**

- answer =
`24`

**Explanation**

If we permute the list to `[5,6,4,3,2,1]`

then `[5, 6]`

sums to `11`

and `[6, 4, 3]`

sums to `13`

.

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