You know that an array has $n$ integers between $1$ and $m$ , and the absolute difference between two adjacent values is at most $1$ .
Given a description of the array where some values may be unknown, your task is to count the number of arrays that match the description.
The first input line has two integers $n$ and $m$ : the array size and the upper bound for each value.
The next line has $n$ integers $x_1,x_2,\dots,x_n$ : the contents of the array. Value $0$ denotes an unknown value.
Print one integer: the number of arrays modulo $10^9+7$ .
3 5 2 0 2· \n · · \n
3\n
The arrays $[2,1,2]$ , $[2,2,2]$ and $[2,3,2]$ match the description.