$10^{100}$ 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.

Input is given from Standard Input in the following format:

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

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

-   $1 \leq N, Q \leq 2 \times 10^5$
-   $1 \leq X \leq 10^9$
-   $1 \leq W_i \leq 10^9 \, (0 \leq i \leq N - 1)$
-   $1 \leq K_i \leq 10^{12} \, (1 \leq i \leq Q)$
-   All values in input are integers.

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 11-st box sealed contains 2 potatoes, and the 2-nd box sealed contains 3 potatoes.