Problem Statement

Find the number of sequences of integers with $N terms, A=(a_1,a_2,\ldots,a_N)$, that satisfy the following conditions, modulo 998244353.

• $0 \leq a_1 \leq a_2 \leq \ldots \leq a_N \leq M$.
• For each $i=1,2,\ldots,N-1$, the remainder when a_i is divided by 3 is different from the remainder when a_{i+1} is divided by 3.

Input

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

Output

Print the answer.

Constraints

• $2 \leq N \leq 10^7$
• $1 \leq M \leq 10^7$
• All values in the input are integers.

Sample Input 1

3 4

Sample Output 1

8

Here are the eight sequences that satisfy the conditions.

• (0,1,2)
• (0,1,3)
• (0,2,3)
• (0,2,4)
• (1,2,3)
• (1,2,4)
• (1,3,4)
• (2,3,4)

Sample Input 2

276 10000000

Sample Output 2

909213205

Be sure to find the count modulo 998244353.

见题面 Input 部分

见题面 Output 部分