A. Carpeting the Room

Codeforces

IDCF100A

Time2000ms

Memory64MB

Difficulty—

implementation

English · Original

Chinese · Translation

Formal · Original

Soroush's room is a square with side length _n_. Before this contest he bought _k_ fine Persian carpets to carpet his room for celebrating the 100th contest on his favorite site. Each Persian carpet is a square of side length _n_1. Soroush wants to cover all the area of his room. Carpets can be put over each other but it is not allowed to rotate the carpets. Can Soroush carpet his room completely? ## Input The input consists of three integer numbers _n_, _k_ and _n_1 (10 ≤ _n_ ≤ 12, 1 ≤ _k_ ≤ 10, ). ## Output Write a single _YES_ or _NO_. Write _YES_ if and only if Sorush can carpet his room completely. [samples]

Soroush 的房间是一个边长为 $n$ 的正方形。在本次比赛之前，他购买了 $k$ 块精美的波斯地毯，准备用它们铺满房间，以庆祝他在最爱的网站上举办的第 $100$ 场比赛。每块波斯地毯都是边长为 $n1$ 的正方形。 Soroush 希望完全覆盖房间的全部面积。地毯可以重叠放置，但不允许旋转地毯。Soroush 能否完全铺满他的房间？输入包含三个整数 $n$、$k$ 和 $n1$（$10 ≤ n ≤ 12$，$1 ≤ k ≤ 10$）。请输出一个 _YES_ 或 _NO_。仅当 Soroush 能够完全铺满房间时，输出 _YES_。 ## Input 输入包含三个整数 $n$、$k$ 和 $n1$（$10 ≤ n ≤ 12$，$1 ≤ k ≤ 10$）。 ## Output 请输出一个 _YES_ 或 _NO_。仅当 Soroush 能够完全铺满房间时，输出 _YES_。 [samples]

**Definitions** Let $ n, k, n_1 \in \mathbb{Z}^+ $ be given integers. **Constraints** $ 10 \leq n \leq 12 $, $ 1 \leq k \leq 10 $, $ n_1 \in \mathbb{Z}^+ $. **Objective** Determine whether the total area of $ k $ carpets, each of side length $ n_1 $, is at least the area of a square room of side length $ n $, under the condition that carpets cannot be rotated and must be aligned axis-aligned. That is, decide if: $$ k \cdot n_1^2 \geq n^2 $$ Output **YES** if the inequality holds, **NO** otherwise.

Samples

Input #1

10 4 6

Output #1

YES

Input #2

10 2 5

Output #2

NO

API Response (JSON)

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    "name": "A. Carpeting the Room",
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    "platform": "Codeforces",
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      "time_limit": 2000,
      "memory_limit": 65536
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      "statement_type": "Markdown",
      "content": "Soroush's room is a square with side length _n_. Before this contest he bought _k_ fine Persian carpets to carpet his room for celebrating the 100th contest on his favorite site. Each Persian carpet i...",
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