201443: [AtCoder]ARC144 D - AND OR Equation

Problem Statement

You are given positive integers $N$ and $K$. Find the number, modulo $998244353$, of integer sequences $\bigl(f(0), f(1), \ldots, f(2^N-1)\bigr)$ that satisfy all of the following conditions:

• $0\leq f(x)\leq K$ for all non-negative integers $x$ ($0\leq x \leq 2^N-1$).
• $f(x) + f(y) = f(x \,\mathrm{AND}\, y) + f(x \,\mathrm{OR}\, y)$ for all non-negative integers $x$ and $y$ ($0\leq x, y \leq 2^N-1$)

Here, $\mathrm{AND}$ and $\mathrm{OR}$ denote the bitwise AND and OR, respectively.

Constraints

• $1\leq N\leq 3\times 10^5$
• $1\leq K\leq 10^{18}$

Input

Input is given from Standard Input in the following format:

$N$ $K$

Output

Print the number, modulo $998244353$, of integer sequences that satisfy the conditions.

Sample Input 1

2 1

Sample Output 1

6

The following six integer sequences satisfy the conditions:

• $(0,0,0,0)$
• $(0,1,0,1)$
• $(0,0,1,1)$
• $(1,0,1,0)$
• $(1,1,0,0)$
• $(1,1,1,1)$

Sample Input 2

2 2

Sample Output 2

19

Sample Input 3

100 123456789123456789

Sample Output 3

34663745