Packing Potatoes

AtCoder

IDabc258_e

Time2000ms

Memory256MB

Difficulty—

$10^{100}$ potatoes are coming from a conveyor belt one by one. The weights of the potatoes are described by a sequence $W = (W_0, \dots, W_{N-1})$ of length $N$: the weight of the $i$\-th potato coming is $W_{(i-1) \bmod N}$, where $(i-1) \bmod N$ denotes the remainder when $i - 1$ is divided by $N$. Takahashi will prepare an empty box and then pack the potatoes in order, as follows. * Pack the incoming potato into the box. If the total weight of the potatoes in the box is now $X$ or greater, seal that box and prepare a new empty box. You are given $Q$ queries. In the $i$\-th query $(1 \leq i \leq Q)$, given a positive integer $K_i$, find the number of potatoes in the $K_i$\-th box to be sealed. It can be proved that, under the Constraints of the problem, there will be at least $K_i$ sealed boxes. ## Constraints * $1 \leq N, Q \leq 2 \times 10^5$ * $1 \leq X \leq 10^9$ * $1 \leq W_i \leq 10^9 \, (0 \leq i \leq N - 1)$ * $1 \leq K_i \leq 10^{12} \, (1 \leq i \leq Q)$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $Q$ $X$ $W_0$ $W_1$ $\ldots$ $W_{N-1}$ $K_1$ $\vdots$ $K_Q$ [samples]

Samples

Input #1

Output #1

2
3

Before sealing the $2$\-nd box, Takahashi will do the following:

*   Prepare an empty box.
*   Pack the $1$\-st potato into the box. Now, the total weight of potatoes in the box is $3$.
*   Pack the $2$\-nd potato into the box. Now, the total weight of potatoes in the box is $3 + 4 = 7$, which is not less than $X = 5$, so seal this box.
*   Prepare a new empty box.
*   Pack the $3$\-rd potato into the box. Now, the total weight of potatoes in the box is $1$.
*   Pack the $4$\-th potato into the box. Now, the total weight of potatoes in the box is $1 + 3 = 4$.
*   Pack the $5$\-th potato into the box. Now, the total weight of potatoes in the box is $1 + 3 + 4 = 8$, which is not less than $X = 5$, so seal this box.

The $1$\-st box sealed contains $2$ potatoes, and the $2$\-nd box sealed contains $3$ potatoes.

Input #2

10 5 20
5 8 5 9 8 7 4 4 8 2
1
1000
1000000
1000000000
1000000000000

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Packing Potatoes",
    "description": {
      "content": "$10^{100}$ potatoes are coming from a conveyor belt one by one. The weights of the potatoes are described by a sequence $W = (W_0, \\dots, W_{N-1})$ of length $N$: the weight of the $i$\\-th potato comi",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc258_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "$10^{100}$ potatoes are coming from a conveyor belt one by one. The weights of the potatoes are described by a sequence $W = (W_0, \\dots, W_{N-1})$ of length $N$: the weight of the $i$\\-th potato comi...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments