- Time limit: 1.00 s
- Memory limit: 512 MB
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.
Input
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.
Output
Print one integer: the number of arrays modulo $10^9+7$.
Constraints
- $1 \le n \le 10^5$
- $1 \le m \le 100$
- $0 \le x_i \le m$
Input:
3 5
2 0 2
Output:
3
Explanation: The arrays $[2,1,2]$, $[2,2,2]$ and $[2,3,2]$ match the description.