Marunomi for All Prefixes

AtCoder

IDttpc2024_2_o

Time2000ms

Memory256MB

Difficulty—

Shobon proposed the following problem: > #### Marunomi > > You are given a sequence of positive integers $W = (w_1, w_2, \dots, w_N)$. > There are $N$ living slimes, named Slime $1, 2, \dots, N$. > Initially, the weight of Slime $i$ ($1 \leq i \leq N$) is $w_i$, and its number of victories is $0$. > You can perform the following operation on the slimes zero or more times: > > * Choose two living slimes, say Slime $i$ and Slime $j$ ($i \neq j$). > * Let the current weight of Slime $i$ be $W_i$ and that of Slime $j$ be $W_j$. > * If $W_i \gt W_j$, the number of victories of Slime $i$ increases by $1$, its weight becomes $W_i + W_j$, and Slime $j$ dies. > * If this condition is not satisfied, nothing happens. > > ![image](https://img.atcoder.jp/ttpc2024_2/38d8d94bdcaac69c081c40d7d91ece34.svg) > For each $i = 1, 2, \dots, N$, let $S_i$ be the maximum number of victories Slime $i$ can achieve through your actions. > Calculate the value of $S_1 + S_2 + \dots + S_N$. However, since this problem is similar to [ARC189 D - Takahashi is Slime](https://atcoder.jp/contests/arc189/tasks/arc189_d), noya2 modified it as follows: > #### Marunomi for All Prefixes > > You are given a sequence of positive integers $A = (a_1, a_2, \dots, a_M)$. > For each $i = 1, 2, \dots, M$, compute the answer to the Marunomi problem when $W = (a_1, a_2, \dots, a_i)$. Solve this problem. ## Constraints * All input values are integers. * $1 \leq M \leq 2 \times 10^5$ * $1 \leq a_i \leq 10^9\ (1 \leq i \leq M)$ ## Input The input is given in the following format: $M$ $a_1$ $a_2$ $\cdots$ $a_M$ [samples]

Samples

Input #1

5
1 2 3 5 20

Output #1

0 1 3 7 11

Input #2

3
1 1 1

Output #2

0 0 0

Input #3

10
17 3467 115 716 9070 32 12251 237 549 17

Output #3

0 1 3 6 10 15 22 29 38 46

API Response (JSON)

{
  "problem": {
    "name": "Marunomi for All Prefixes",
    "description": {
      "content": "Shobon proposed the following problem: > #### Marunomi >  > You are given a sequence of positive integers $W = (w_1, w_2, \\dots, w_N)$. > There are $N$ living slimes, named Slime $1, 2, \\dots, N$.   ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "ttpc2024_2_o"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Shobon proposed the following problem:\n\n> #### Marunomi\n> \n> You are given a sequence of positive integers $W = (w_1, w_2, \\dots, w_N)$.\n> There are $N$ living slimes, named Slime $1, 2, \\dots, N$.  \n...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments