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Points:
5 (partial)

Time limit:
2.0s

Memory limit:
64M

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Problem type

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Given points in dimensional space, find the minimum "surface area" of a hyperrectangle required to contain all points modulo .

As an example, the "surface area" of a -dimensional hyperrectangle (rectangle) is the sum of its side lengths. The "surface area" of a -dimensional hyperrectangle (rectangular prism) is the sum of the areas of the sides of the hyperrectangle.

#### Input Specification

The first line will contain two space-separated integers, , the number of dimensions and the number of points respectively.

The next lines will each contain integers, .

#### Output Specification

Output the minimum "surface area" of a hyperrectangle required to contain all points, modulo .

#### Subtasks

##### Subtask 1 [10%]

##### Subtask 2 [20%]

##### Subtask 3 [70%]

No further constraints.

#### Sample Input 1

```
2 4
1 1
3 3
-1 2
0 0
```

#### Sample Output 1

`14`

#### Sample Input 2

```
5 3
1 4 2 3 4
0 -129 6 9 0
0 0 -10 9 5
```

#### Sample Output 2

`183436`

## Comments