201163: [AtCoder]ARC116 D - I Wanna Win The Game

Problem Statement

Given are integers $N$ and $M$. How many sequences $A$ of $N$ integers satisfy the following conditions?

• $0 \leq A_i \left(i = 1, 2, \ldots, N\right)$
• $\sum_{i = 1}^{N} A_i = M$
• $A_1$ xor $A_2$ xor $\cdots$ xor $A_N = 0$ ("xor" denotes the bitwise XOR.)

Since the answer can be enormous, report it modulo $998244353$.

Constraints

• All values in input are integers.
• $1 \leq N \leq 5000$
• $1 \leq M \leq 5000$

Input

Input is given from Standard Input in the following format:

$N$ $M$

Output

Print the answer.

Sample Input 1

5 20

Sample Output 1

475

Some of the sequences $A$ satisfying the conditions follow:

• $A = \left(10, 0, 10, 0, 0\right)$
• $A = \left(1, 2, 3, 7, 7\right)$

Sample Input 2

10 5

Sample Output 2

0

Sample Input 3

3141 2718

Sample Output 3

371899128