Problem Statement

We define the general term $a_n$ of a sequence $a_0, a_1, a_2, \\dots$ by:

$a_n = \\begin{cases} 1 & (0 \\leq n \\lt K) \\\\ \\displaystyle{\\sum_{i=1}^K} a_{n-i} & (K \\leq n). \\\\ \\end{cases}$

Given an integer $N$, find the sum, modulo $998244353$, of $a_m$ over all non-negative integers $m$ such that $m\\text{ AND }N = m$. ($\\text{AND}$ denotes the bitwise AND.)

What is bitwise AND? The bitwise AND of non-negative integers $A$ and $B$, $A\\text{ AND }B$, is defined as follows.
・When $A\\text{ AND }B$ is written in binary, its $2^k$s place ($k \\geq 0$) is $1$ if $2^k$s places of $A$ and $B$ are both $1$, and $0$ otherwise.

Constraints

• $1 \\leq K \\leq 5 \\times 10^4$
• $0 \\leq N \\leq 10^{18}$
• $N$ and $K$ are integers.

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Input

The input is given from Standard Input in the following format:

$K$ $N$

Output

Print the answer.

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Sample Input 1

2 6

Sample Output 1

21

$a_0$ and succeeding terms are $1, 1, 2, 3, 5, 8, 13, 21, \\dots$. Four non-negative integers, $0, 2, 4$, and $6$, satisfy $6 \\text{ AND } m = m$, so the answer is $1 + 2 + 5 + 13 = 21$.

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Sample Input 2

2 8

Sample Output 2

35

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Sample Input 3

1 123456789

Sample Output 3

65536

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Sample Input 4

300 20230429

Sample Output 4

125461938

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Sample Input 5

42923 999999999558876113

Sample Output 5

300300300