Make Multiples

AtCoder

IDarc166_b

Time2000ms

Memory256MB

Difficulty—

You are given an integer sequence $A=(A_1,\ldots,A_N)$ and positive integers $a$, $b$, and $c$. You can perform the following operation on this sequence any number of times, possibly zero. * Choose an integer $i$ such that $1\leq i\leq N$. Replace $A_i$ with $A_i+1$. Your objective is to make the sequence $A$ contain at least one multiple of $a$, at least one multiple of $b$, and at least one multiple of $c$. Find the minimum number of operations required to achieve this objective. ## Constraints * $1\leq N\leq 2\times 10^5$ * $1\leq a, b, c \leq 10^6$ * $1\leq A_i\leq 10^{18}$ ## Input The input is given from Standard Input in the following format: $N$ $a$ $b$ $c$ $A_1$ $\cdots$ $A_N$ [samples]

Samples

Input #1

3 3 4 5
8 9 11

Output #1

2

You can perform the operation twice so that $A = (8,10,12)$ to achieve the objective.

Input #2

3 3 4 5
14 11 59

Output #2

1

You can perform the operation once so that $A = (14,11,60)$ to achieve the objective.

Input #3

6 10 20 30
8 17 5 28 39 13

Output #3

3

You can perform the operation three times so that $A = (8,17,5,30,40,13)$ to achieve the objective.

Input #4

1 999997 999998 999999
123456789123456789

Output #4

876537210887543205

You can perform the operation $876537210887543205$ times so that $A = (999994000010999994)$ to achieve the objective.

API Response (JSON)

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  "problem": {
    "name": "Make Multiples",
    "description": {
      "content": "You are given an integer sequence $A=(A_1,\\ldots,A_N)$ and positive integers $a$, $b$, and $c$. You can perform the following operation on this sequence any number of times, possibly zero. *   Choose",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc166_b"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given an integer sequence $A=(A_1,\\ldots,A_N)$ and positive integers $a$, $b$, and $c$.\nYou can perform the following operation on this sequence any number of times, possibly zero.\n\n*   Choose...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments