### Problem Statement

You will be given a int[] A that contains N elements and an int P. Return the number of distinct integer values of X for which the following inequality is true:

```|A0 - X| + |A1 - X| + ... + |AN-1 - X| ≤ P
```

### Definition

 Class: ModularInequality Method: countSolutions Parameters: int[], int Returns: int Method signature: int countSolutions(int[] A, int P) (be sure your method is public)

### Constraints

-A will contain between 1 and 50 elements, inclusive.
-Each element of A will be between -1,000,000,000 and 1,000,000,000 inclusive.
-P will be between 0 and 1,000,000,000 inclusive.

### Examples

0)

 `{1, 2, 3}` `6`
`Returns: 5`
 The possible values for X are 0, 1, 2, 3 and 4.
1)

 `{10, 30, 15, -1, 17}` `42`
`Returns: 7`
2)

 `{0, 2, 3, -5, 10}` `17`
`Returns: 0`
3)

 `{-693}` `1265`
`Returns: 2531`
4)

 `{965, -938, -396, -142, 926, 31, -720}` `6495`
`Returns: 1781`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=6765

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=10005&pm=6765

Andrew_Lazarev

#### Testers:

PabloGilberto , brett1479 , Yarin , Olexiy

Geometry, Math