Problem Statement

You are given positive integers $N$ and $M$.

Find the number of sequences $A=(A_1,\\ A_2,\\ \\dots,\\ A_N)$ of $N$ positive integers that satisfy the following conditions, modulo $998244353$.

• $1 \\leq A_1 < A_2 < \\dots < A_N \\leq M$.
• $B_1 < B_2 < \\dots < B_N$, where $B_i = A_1 \\oplus A_2 \\oplus \\dots \\oplus A_i$.

Here, $\\oplus$ denotes bitwise $\\mathrm{XOR}$.

What is bitwise $\\mathrm{XOR}$?

The bitwise $\\mathrm{XOR}$ of non-negative integers $A$ and $B$, $A \\oplus B$, is defined as follows:

• When $A \\oplus B$ is written in base two, the digit in the $2^k$'s place ($k \\geq 0$) is $1$ if exactly one of $A$ and $B$ is $1$, and $0$ otherwise.

For example, we have $3 \\oplus 5 = 6$ (in base two: $011 \\oplus 101 = 110$).
Generally, the bitwise $\\mathrm{XOR}$ of $k$ non-negative integers $p_1, p_2, p_3, \\dots, p_k$ is defined as $(\\dots ((p_1 \\oplus p_2) \\oplus p_3) \\oplus \\dots \\oplus p_k)$. We can prove that this value does not depend on the order of $p_1, p_2, p_3, \\dots, p_k$.

Constraints

• $1 \\leq N \\leq M < 2^{60}$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $M$

Output

Print the answer.

Sample Input 1

2 4

Sample Output 1

5

For example, $(A_1,\\ A_2)=(1,\\ 3)$ counts, since $A_1 < A_2$ and $B_1 < B_2$ where $B_1=A_1=1,\\ B_2=A_1\\oplus A_2=2$.

The other pairs that count are $(A_1,\\ A_2)=(1,\\ 2),\\ (1,\\ 4),\\ (2,\\ 4),\\ (3,\\ 4)$.

Sample Input 2

4 4

Sample Output 2

0

Sample Input 3

10 123456789

Sample Output 3

205695670