A. Paper Airplanes

Codeforces

IDCF965A

Time1000ms

Memory256MB

Difficulty—

math

English · Original

Chinese · Translation

Formal · Original

To make a paper airplane, one has to use a rectangular piece of paper. From a sheet of standard size you can make $s$ airplanes. A group of $k$ people decided to make $n$ airplanes each. They are going to buy several packs of paper, each of them containing $p$ sheets, and then distribute the sheets between the people. Each person should have enough sheets to make $n$ airplanes. How many packs should they buy? ## Input The only line contains four integers $k$, $n$, $s$, $p$ ($1 \le k, n, s, p \le 10^4$) — the number of people, the number of airplanes each should make, the number of airplanes that can be made using one sheet and the number of sheets in one pack, respectively. ## Output Print a single integer — the minimum number of packs they should buy. [samples] ## Note In the first sample they have to buy $4$ packs of paper: there will be $12$ sheets in total, and giving $2$ sheets to each person is enough to suit everyone's needs. In the second sample they have to buy a pack for each person as they can't share sheets.

要制作一架纸飞机，需要使用一张矩形纸。从一张标准尺寸的纸张上可以制作 $s$ 架飞机。一组 $k$ 个人决定每人制作 $n$ 架飞机。他们打算购买若干包纸，每包包含 $p$ 张纸，然后将纸张分发给每个人。每个人应有足够的纸张来制作 $n$ 架飞机。他们至少需要购买多少包纸？仅一行包含四个整数 $k$, $n$, $s$, $p$ ($1 lt.eq k, n, s, p lt.eq 10^4$) — 分别表示人数、每人应制作的飞机数、一张纸可制作的飞机数、每包纸的张数。请输出一个整数 —— 他们应购买的最少包数。在第一个测试用例中，他们需要购买 $4$ 包纸：总共会有 $12$ 张纸，每人分得 $2$ 张纸已足够满足需求。在第二个测试用例中，他们必须为每人购买一包纸，因为他们不能共享纸张。 ## Input 仅一行包含四个整数 $k$, $n$, $s$, $p$ ($1 lt.eq k, n, s, p lt.eq 10^4$) — 分别表示人数、每人应制作的飞机数、一张纸可制作的飞机数、每包纸的张数。 ## Output 请输出一个整数 —— 他们应购买的最少包数。 [samples] ## Note 在第一个测试用例中，他们需要购买 $4$ 包纸：总共会有 $12$ 张纸，每人分得 $2$ 张纸已足够满足需求。在第二个测试用例中，他们必须为每人购买一包纸，因为他们不能共享纸张。

**Definitions** Let $ k \in \mathbb{Z}^+ $: number of people. Let $ n \in \mathbb{Z}^+ $: number of airplanes each person must make. Let $ s \in \mathbb{Z}^+ $: number of airplanes producible per sheet. Let $ p \in \mathbb{Z}^+ $: number of sheets per pack. **Constraints** $ 1 \leq k, n, s, p \leq 10^4 $ **Objective** Compute the minimum number of packs $ x \in \mathbb{Z}^+ $ such that the total number of sheets $ x \cdot p $ is sufficient to provide each of the $ k $ people with at least $ \left\lceil \frac{n}{s} \right\rceil $ sheets. That is, find the smallest integer $ x $ satisfying: $$ x \cdot p \geq k \cdot \left\lceil \frac{n}{s} \right\rceil $$ Thus, $$ x = \left\lceil \frac{k \cdot \left\lceil \frac{n}{s} \right\rceil}{p} \right\rceil $$

Samples

Input #1

5 3 2 3

Output #1

Input #2

5 3 100 1

Output #2

API Response (JSON)

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      "content": "To make a paper airplane, one has to use a rectangular piece of paper. From a sheet of standard size you can make $s$ airplanes.\n\nA group of $k$ people decided to make $n$ airplanes each. They are goi...",
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      "content": "要制作一架纸飞机，需要使用一张矩形纸。从一张标准尺寸的纸张上可以制作 $s$ 架飞机。\n\n一组 $k$ 个人决定每人制作 $n$ 架飞机。他们打算购买若干包纸，每包包含 $p$ 张纸，然后将纸张分发给每个人。每个人应有足够的纸张来制作 $n$ 架飞机。他们至少需要购买多少包纸？\n\n仅一行包含四个整数 $k$, $n$, $s$, $p$ ($1 lt.eq k, n, s, p lt.eq 10^...",
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