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$y (0\leq x, y \leq 2^N-1)$

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

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.

Constraints

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

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

见题面 Input 部分

见题面 Output 部分