Problem Statement

Given is a sequence of $A+B integers (X_1,X_2,\cdots,X_{A+B}), which contains exactly A$ ones and exactly B twos.
Snuke has a set s, which is initially empty.
He is going to do A+B operations.
The i-th operation is as follows.

• If X_i=1: Choose an integer v such that $1 \leq v \leq A$ and add it to s.
  Here, v must not be an integer that was chosen in a previous operation.

• If X_i=2: Delete from s the element with the largest value.
  The input guarantees that s is not empty just before this operation.

How many sets are there that can be the final state of s?
Find the count modulo 998244353.

Input

Input is given from Standard Input in the following format:
A B
$X_1 X_2 \cdots X_{A+B}$

Output

Print the answer modulo 998244353.

Constraints

• $1 \leq A \leq 5000$
• $0 \leq B \leq A-1$
• $1 \leq X_i \leq 2$
• X_i=1 for exactly A indices i.
• X_i=2 for exactly B indices i.
• s will not be empty just before an operation with X_i=2.
• All values in input are integers.

Sample Input 1

3 1
1 1 2 1

Sample Output 1

2

There are two possible final states of s: s={1,2},{1,3}.
For example, the following sequence of operations results in s={1,3}.

• i=1: Add 2 to s.
• i=2: Add 1 to s.
• i=3: Delete 2 from s.
• i=4: Add 3 to s.

Sample Input 2

20 6
1 1 1 1 1 2 1 1 1 2 1 2 1 2 1 2 1 1 1 1 2 1 1 1 1 1

Sample Output 2

5507

见题面 Input 部分

见题面 Output 部分