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.

Input

Input is given from Standard Input in the following format:
N M

Output

Print the answer.

Constraints

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

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

见题面 Input 部分

见题面 Output 部分