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 $3$.

Constraints

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

Input

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

$N$ $M$

Output

Print the answer.

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 $998244353$.