{"raw_statement":[{"iden":"problem statement","content":"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:\n\n*   $f(S,a) = \\sum_{i=1}^{k} S_i \\times a^{k - i}$.\n\nFor example, $f((1,2,3),4) = 1 \\times 4^2 + 2 \\times 4^1 + 3 \\times 4^0 = 27$, and $f((1,1,1,1),10) = 1 \\times 10^3 + 1 \\times 10^2 + 1 \\times 10^1 + 1 \\times 10^0 = 1111$.\nYou 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.\n\n*   $k \\ge 1$\n*   $a,b \\le N$\n*   $S_1 \\neq 0$\n*   $S_i < \\min(10,a,b)(1 \\le i \\le k)$\n*   $f(S,a) - f(S,b) = X$"},{"iden":"constraints","content":"*   $1 \\le N \\le 10^9$\n*   $1 \\le X \\le 2 \\times 10^5$\n*   All input values are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$ $X$"},{"iden":"sample input 1","content":"4 2"},{"iden":"sample output 1","content":"5\n\nThe 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."},{"iden":"sample input 2","content":"9 30"},{"iden":"sample output 2","content":"31"},{"iden":"sample input 3","content":"322322322 200000"},{"iden":"sample output 3","content":"140058961"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}