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