Gromozeka's favorite chess piece is the rook. But he likes to walk her only vertically, and either one cell or two. Gromozeka ends the game when the rook reaches the end of the file. Thinking about the next position, he noticed that some cells on the path of the rook are under attack from the opponent's pieces and it is impossible to move on these cells.
Help Gromozeka calculate in how many ways he can move his rook to the other end of the chessboard without hitting the squares under attack.
Input
The first line contains one natural number
N (N <= 40): the size of the chess field. The second line contains one natural number
K (K <= N ): the number of cells under attack. The third line contains
K different natural numbers in the range from
1 to
N: the numbers of the squares under attack by the opponent's pieces.
Imprint
Output one number - the number of ways to get to the end of the vertical (to the
N-th cell).
Examples
| # |
Input |
Output |
| 1 |
7
2
3 5
| 2 |
| 2 |
10
3
5 1 2
| 0 |
| 3 |
3
1
2 |
1 |