Many CRT

AtCoder

IDagc063_d

Time2000ms

Memory256MB

Difficulty—

You are given positive integers $N, a, b, c, d$. Determine whether there is a non-negative integer $x$ such that $x\equiv a+kb \pmod{c+kd}$ for every $k=0,1,\ldots,N-1$. If it exists, find the smallest such $x$ modulo $998244353$. ## Constraints * $2\leq N\leq 10^6$ * $1\leq a,b,c,d\leq 10^6$ ## Input The input is given from Standard Input in the following format: $N$ $a$ $b$ $c$ $d$ [samples]

Samples

Input #1

2 1 2 3 4

Output #1

10

$x=10$ is the smallest non-negative integer such that $x\equiv 1\pmod{3}$ and $x\equiv 3\pmod{7}$.

Input #2

2 1 1 10 10

Output #2

\-1

No non-negative integer $x$ satisfies $x\equiv 1\pmod{10}$ and $x\equiv 2\pmod{20}$.

Input #3

100 20 30 2 3

Output #3

0

$x= 0$ is the smallest non-negative integer satisfying the condition.

Input #4

9 12 34 56 78

Output #4

827501367

$x=15977769171609124$ is the smallest non-negative integer satisfying the condition.

API Response (JSON)

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    "name": "Many CRT",
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      "content": "You are given positive integers $N, a, b, c, d$. Determine whether there is a non-negative integer $x$ such that $x\\equiv a+kb \\pmod{c+kd}$ for every $k=0,1,\\ldots,N-1$. If it exists, find the smalles",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
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    "difficulty": "None",
    "is_remote": true,
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    "sign": "agc063_d"
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    {
      "statement_type": "Markdown",
      "content": "You are given positive integers $N, a, b, c, d$.\nDetermine whether there is a non-negative integer $x$ such that $x\\equiv a+kb \\pmod{c+kd}$ for every $k=0,1,\\ldots,N-1$. If it exists, find the smalles...",
      "is_translate": false,
      "language": "English"
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Full JSON Raw Segments