Max Add

AtCoder

IDarc120_a

Time2000ms

Memory256MB

Difficulty—

For a sequence $a = (a_1, a_2, a_3, \dots, a_k)$, let $f(a)$ be the sum of its elements after the following is done: * For each $i = 1, 2, 3, \dots, k$, in this order, do the following operation: add the current maximum value of an element in $a$ to $a_i$. You are given a sequence of length $N$: $A = (A_1, A_2, A_3, \dots, A_N)$. For each integer $k$ between $1$ and $N$ (inclusive), find $f(a)$ when $a = (A_1, A_2, A_3, \dots, A_k)$. ## Constraints * $1 \le N \le 2 \times 10^5$ * $1 \le A_i \le 10^7$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $A_3$ $\dots$ $A_N$ [samples]

Samples

Input #1

3
1 2 3

Output #1

2
8
19

For example, when $a = (A_1, A_2, A_3)$, $f(a)$ is computed as follows:

*   First, for $i = 1$, add to $a_1$ the current maximum value of $a$, which is $3$, making $a = (4, 2, 3)$.
*   Next, for $i = 2$, add to $a_2$ the current maximum value of $a$, which is $4$, making $a = (4, 6, 3)$.
*   Finally, for $i = 3$, add to $a_3$ the current maximum value of $a$, which is $6$, making $a = (4, 6, 9)$.
*   $f(a)$ is the sum of the elements of $a$ now, which is $19$.

API Response (JSON)

{
  "problem": {
    "name": "Max Add",
    "description": {
      "content": "For a sequence $a = (a_1, a_2, a_3, \\dots, a_k)$, let $f(a)$ be the sum of its elements after the following is done: *   For each $i = 1, 2, 3, \\dots, k$, in this order, do the following operation:  ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc120_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "For a sequence $a = (a_1, a_2, a_3, \\dots, a_k)$, let $f(a)$ be the sum of its elements after the following is done:\n\n*   For each $i = 1, 2, 3, \\dots, k$, in this order, do the following operation:  ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments