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Contest: Task: Related: TaskD TaskF

Score : $500$ points

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