Integer Division

AtCoder

IDabc288_f

Time2000ms

Memory256MB

Difficulty—

You are given a positive integer $X$ with $N$ digits in decimal representation. None of the digits of $X$ is $0$. For a subset $S$ of $\lbrace 1,2, \ldots, N-1 \rbrace $ , let $f(S)$ be defined as follows. > See the decimal representation of $X$ as a string of length $N$, and decompose it into $|S| + 1$ strings by splitting it between the $i$\-th and $(i + 1)$\-th characters if and only if $i \in S$. > Then, see these $|S| + 1$ strings as integers in decimal representation, and let $f(S)$ be the product of these $|S| + 1$ integers. There are $2^{N-1}$ subsets of $\lbrace 1,2, \ldots, N-1 \rbrace $ , including the empty set, which can be $S$. Find the sum of $f(S)$ over all these $S$, modulo $998244353$. ## Constraints * $2 \leq N \leq 2 \times 10^5$ * $X$ has $N$ digits in decimal representation, none of which is $0$. * All values in the input are integers. ## Input The input is given from Standard Input in the following format: $N$ $X$ [samples]

Samples

Input #1

3
234

Output #1

418

For $S = \emptyset$, we have $f(S) = 234$.  
For $S = \lbrace 1 \rbrace$, we have $f(S) = 2 \times 34 = 68$.  
For $S = \lbrace 2 \rbrace$, we have $f(S) = 23 \times 4 = 92$.  
For $S = \lbrace 1, 2 \rbrace$, we have $f(S) = 2 \times 3 \times 4 = 24$.  
Thus, you should print $234 + 68 + 92 + 24 = 418$.

Input #2

4
5915

Output #2

Input #3

9
998244353

Output #3

258280134

API Response (JSON)

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  "problem": {
    "name": "Integer Division",
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      "content": "You are given a positive integer $X$ with $N$ digits in decimal representation. None of the digits of $X$ is $0$.   For a subset $S$ of $\\lbrace 1,2, \\ldots, N-1 \\rbrace $ , let $f(S)$ be defined as f",
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      "memory_limit": 262144
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    "difficulty": "None",
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      "statement_type": "Markdown",
      "content": "You are given a positive integer $X$ with $N$ digits in decimal representation. None of the digits of $X$ is $0$.  \nFor a subset $S$ of $\\lbrace 1,2, \\ldots, N-1 \\rbrace $ , let $f(S)$ be defined as f...",
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      "language": "English"
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