You are given $N$ bricks that are numbered from $1$ to $N$. You are required to color all the bricks. Here, $K$ bricks are already colored.

You can only color the $i^{th}$ brick if the $(i+1)^{th}$ or $(i-1)^{th}$ brick is already colored. Your task is to determine the number of ways you can color all the remaining bricks. Since the number of ways can be very large, therefore print the number of ways modulo $1000000007$.
Input format

• First line: Two space-separated integer $N,\ K$
• Second line: $K$ space-separated integers each denoting the brick that is already colored

Output format

Print an integer denoting the number of ways to color the remaining bricks modulo $1000000007$.

Constraints

$1\le K\le N\le1000$