Problem Description

You are given a pair of integer sequences of length $N$, $A=(A_1, A_2, \dots, A_N)$ and $B=(B_1, B_2, \dots, B_N)$. Initially, for all $i = 1, 2, \dots, N$, $A_i = B_i = 0$.

You will perform the following operation $M$ times on $A$ and $B$:

• Operation: Choose integers $i, j$ ($1 \le i, j \le N$), and increment $A_i$ and $B_j$ by $1$.

However, among the $M$ operations, exactly $X$ operations must satisfy $i = j$.

Find the number of possible pairs of sequences $A$ and $B$ after $M$ operations, modulo $998244353$.

Input Format

The input is given from the standard input in the following format:

$N\ M\ X$

Output Format

Output the number of possible pairs of sequences $A$ and $B$ after $M$ operations, modulo $998244353$.

Sample Input and Output

Sample Input #1

3 1 1

Sample Output #1

3

Sample Input #2

3 1 0

Sample Output #2

6

Sample Input #3

4 4 2

Sample Output #3

643

Sample Input #4

314 1592 653

Sample Output #4

755768689

Notes/Hints

Constraints

• $2 \leq N \leq 3000$
• $0 \leq X \leq M \leq 3000$
• All inputs are integers

Sample Explanation 1

The following $3$ pairs:
- $A=(1,0,0), B=(1,0,0)$
- $A=(0,1,0), B=(0,1,0)$
- $A=(0,0,1), B=(0,0,1)$

Sample Explanation 2

The following $6$ pairs:
- $A=(1,0,0), B=(0,1,0)$
- $A=(1,0,0), B=(0,0,1)$
- $A=(0,1,0), B=(1,0,0)$
- $A=(0,1,0), B=(0,0,1)$
- $A=(0,0,1), B=(1,0,0)$
- $A=(0,0,1), B=(0,1,0)$

Sample Explanation 3

For example, the following pairs of $A$ and $B$ are possible:
- $A=(1,1,1,1), B=(1,1,1,1)$
- $A=(1,0,0,3), B=(0,1,0,3)$

见题面 Input 部分

见题面 Output 部分