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~ .