102584: [AtCoder]ABC258 E - Packing Potatoes

Problem Statement

$10^{100}$ 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:

$N$ $Q$ $X$
$W_0$ $W_1$ $\ldots$ $W_{N-1}$
$K_1$
$\vdots$
$K_Q$

Output

Print $Q$ lines. The $i$-th line $(1 \leq i \leq Q)$ should contain the answer to the $i$-th query.

Sample Input 1

3 2 5
3 4 1
1
2

Sample 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.

Sample Input 2

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

Sample Output 2

4
5
5
5
5

问题描述

有一个传送带会逐一地运送$10^{100}$个土豆。这些土豆的重量可以用长度为$N$的序列$W = (W_0, \dots, W_{N-1})$来描述：第$i$个运来的土豆的重量是$W_{(i-1) \bmod N}$，其中$(i-1) \bmod N$表示将$i - 1$除以$N$的余数。

高桥将会准备一个空箱子，然后按照顺序将土豆装入，如下所示。

• 将运来的土豆装入箱子。如果现在箱子中土豆的总重量是$X$或更大，那么将这个箱子密封起来，并准备一个新的空箱子。

你将收到$Q$个查询。在第$i$个查询$(1 \leq i \leq Q)$中，给定一个正整数$K_i$，找出将要被密封的第$K_i$个箱子中的土豆数量。可以证明，在问题的约束下，至少会有$K_i$个被密封的箱子。

约束

• $1 \leq N, Q \leq 2 \times 10^5$
• $1 \leq X \leq 10^9$
• $1 \leq W_i \leq 10^9 \, (0 \leq i \leq N - 1)$
• $1 \leq K_i \leq 10^{12} \, (1 \leq i \leq Q)$
• 输入中的所有值都是整数。

输入

输入将从标准输入中给出以下格式：

$N$ $Q$ $X$
$W_0$ $W_1$ $\ldots$ $W_{N-1}$
$K_1$
$\vdots$
$K_Q$

输出

打印$Q$行。第$i$行$(1 \leq i \leq Q)$应包含第$i$个查询的答案。

样例输入1

3 2 5
3 4 1
1
2

样例输出1

2
3

在密封第二个箱子之前，高桥将会做以下事情：

• 准备一个空箱子。
• 将第1个土豆装入箱子。现在，箱子中土豆的总重量是$3$。
• 将第2个土豆装入箱子。现在，箱子中土豆的总重量是$3 + 4 = 7$，这并不小于$X = 5$，所以将这个箱子密封起来。
• 准备一个新的空箱子。
• 将第3个土豆装入箱子。现在，箱子中土豆的总重量是$1$。
• 将第4个土豆装入箱子。现在，箱子中土豆的总重量是$1 + 3 = 4$。
• 将第5个土豆装入箱子。现在，箱子中土豆的总重量是$1 + 3 + 4 = 8$，这并不小于$X = 5$，所以将这个箱子密封起来。

被密封的第一个箱子中包含2个土豆，被密封的第二个箱子中包含3个土豆。

样例输入2

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

样例输出2

4
5
5
5
5