Village of M People

AtCoder

IDarc118_b

Time2000ms

Memory256MB

Difficulty—

The Republic of ARC has $N$ citizens, all of whom play competitive programming. Each citizen is given a dan _(grade)_ which is $1$, $2$, $\ldots$, or $K$, according to their skill. A national census has revealed that there are exactly $A_i$ citizens with dan $i$. To make this data easier to understand, the king has decided to describe the country as if it were a village of $M$ people. Set the number of people with dan $i$ in the village, $B_i$, so that $\max_i\left|\frac{B_i}{M} - \frac{A_i}{N}\right|$ is minimized, while satisfying the following: * each $B_i$ is a non-negative integer, satisfying $\sum_{i=1}^K B_i = M$. Print one such way to set $B = (B_1, B_2, \ldots, B_K)$. ## Constraints * $1\leq K\leq 10^5$ * $1\leq N, M\leq 10^9$ * Each $A_i$ is a non-negative integer satisfying $\sum_{i=1}^K A_i = N$. ## Input Input is given from Standard Input in the following format: $K$ $N$ $M$ $A_1$ $A_2$ $\ldots$ $A_K$ [samples]

Samples

Input #1

3 7 20
1 2 4

Output #1

3 6 11

In this output, we have $\max_i\left|\frac{B_i}{M} - \frac{A_i}{N}\right| = \max\left(\left|\frac{3}{20}-\frac{1}{7}\right|, \left|\frac{6}{20}-\frac{2}{7}\right|, \left|\frac{11}{20}-\frac{4}{7}\right|\right) = \max\left(\frac{1}{140}, \frac{1}{70}, \frac{3}{140}\right) = \frac{3}{140}$.

Input #2

3 3 100
1 1 1

Output #2

34 33 33

Note that $B_1 = B_2 = B_3 = 33$ does not satisfy the requirement, since the sum must be $M = 100$.
In this sample, other than `34 33 33`, printing `33 34 33` or `33 33 34` will also be accepted.

Input #3

6 10006 10
10000 3 2 1 0 0

Output #3

10 0 0 0 0 0

Input #4

7 78314 1000
53515 10620 7271 3817 1910 956 225

Output #4

683 136 93 49 24 12 3

API Response (JSON)

{
  "problem": {
    "name": "Village of M People",
    "description": {
      "content": "The Republic of ARC has $N$ citizens, all of whom play competitive programming. Each citizen is given a dan _(grade)_ which is $1$, $2$, $\\ldots$, or $K$, according to their skill. A national census h",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc118_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "The Republic of ARC has $N$ citizens, all of whom play competitive programming. Each citizen is given a dan _(grade)_ which is $1$, $2$, $\\ldots$, or $K$, according to their skill.\nA national census h...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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