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.