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 $p_1, p_2, p_3, \dots, p_k$.
  

Input

Input is given from Standard Input in the following format:
N M

Output

Print the answer.

Constraints

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

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

见题面 Input 部分

见题面 Output 部分