### Problem Statement

John and Brus are going to a theater to see a very interesting movie. They would like to have seats next to each other in the same row. The theater contains n rows, with m seats in each row. Rows are numbered 1 to n from front to back, and seats are numbered 1 to m from left to right. Some of the seats are already reserved, but John and Brus can book any of the available seats.

You are given int[]s row and seat. The i-th elements of row and seat are the row number and seat number of the i-th reserved seat. All remaining seats are available. Return the number of ways for John and Brus to book two available seats next to each other in the same row.

### Definition

 Class: TheMoviesLevelOneDivOne Method: find Parameters: int, int, int[], int[] Returns: long Method signature: long find(int n, int m, int[] row, int[] seat) (be sure your method is public)

### Notes

-Two bookings are considered different only if one contains a seat that the other does not contain. In other words, they don't need to decide which seat John sits in and which seat Brus sits in.

### Constraints

-n and m will each be between 1 and 1,000,000,000, inclusive.
-row will contain between 1 and 47 elements, inclusive.
-row and seat will contain the same number of elements.
-Each element of row will be between 1 and n, inclusive.
-Each element of seat will be between 1 and m, inclusive.
-All pairs (row[i], seat[i]) will be distinct.

### Examples

0)

 `2` `3` `{1, 2}` `{2, 3}`
`Returns: 1`
 The first and the second seat in the second row are the only two free seats next to each other in the same row.
1)

 `2` `3` `{1, 1, 1, 2, 2, 2}` `{1, 2, 3, 1, 2, 3}`
`Returns: 0`
 There are no free seats in the theater.
2)

 `4` `7` `{1}` `{1}`
`Returns: 23`
3)

 `10` `8` `{1, 9, 6, 10, 6, 7, 9, 3, 9, 2}` `{7, 7, 3, 3, 7, 1, 5, 1, 6, 2}`
`Returns: 54`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=10898

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=14152&pm=10898

Vasyl[alphacom]

#### Testers:

PabloGilberto , Andrew_Lazarev , ivan_metelsky

Simple Math