Problem Statement

For $a non-negative integer sequence S=(S_1,S_2,\dots,S_k)$ and an integer a, we define the function f(S,a) as follows:

• $f(S,a) = \sum_{i=1}^{k} S_i \times a^{k - i}$.

For example$, f((1,2,3),4) = 1 \times 4^2 + 2 \times 4^1 + 3 \times 4^0 = 27$, and $f((1,1,1,1),10) = 1 \times 10^3 + 1 \times 10^2 + 1 \times 10^1 + 1 \times 10^0 = 1111$.
You are given positive integers N and X. Find the number, modulo 998244353, of triples (S,a,b) of a sequence of $non-negative integers S=(S_1,S_2,\dots,S_k)$ and positive integers a and b that satisfy all of the following conditions.

• $k \ge 1$
• $a,b \le N$
• $S_1 \neq 0$
• $S_i < \min(10,a,b)(1 \le i \le k)$
• f(S,a) - f(S,b) = X

Input

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

Output

Print the number, modulo 998244353, of triples (S,a,b) of a sequence of $non-negative integers S=(S_1,S_2,\dots,S_k)$ and positive integers a and b that satisfy the conditions.

Constraints

• $1 \le N \le 10^9$
• $1 \le X \le 2 \times 10^5$
• All input values are integers.

Sample Input 1

4 2

Sample Output 1

5

The five triples (S,a,b)=((1,0),4,2),((1,1),4,2),((2,0),4,3),((2,1),4,3),((2,2),4,3) satisfy the conditions.

Sample Input 2

9 30

Sample Output 2

31

Sample Input 3

322322322 200000

Sample Output 3

140058961

见题面 Input 部分

见题面 Output 部分