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.