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No.159 The USB That Won't Go In

レベル : / AI推定難易度 : 500 / 実行時間制限 : 1ケース 1.000秒 / メモリ制限 : 64 MB / 標準ジャッジ問題
タグ : （AC するまで非表示） / 解いたユーザー数 469
作問者 : ぴろず
お気に入りにしたユーザー ProblemId : 405 / 自分の提出
問題文最終更新日: 2026-06-26 10:14:07
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Problem Statement

It is sometimes said of USB (connectors) that "it goes in after flipping it over 2 times."
When Taro plugs in a USB, he follows the procedure below.

  1. Initially, the USB is face up with probability $p$ and face down with probability $(1-p)$.
  2. He tries to plug in the USB. When the USB is face up, it goes in with probability $q$ and does not go in with probability $(1-q)$. When the USB is face down, it does not go in.
  3. If the USB did not go in, he flips it over, from face up to face down or from face down to face up, and returns to step 2. If the USB went in, the procedure ends.
Each attempt to plug in the USB may be considered independent.

Let $P_i$ denote the probability that the procedure ends after flipping the USB exactly $i$ times. Taro is curious about when $P_1 < P_2$ holds.
Given $p,q$, write a program that outputs $YES$ if $P_1 < P_2$, and $NO$ otherwise.

Input

p q

$p,q$ are given on $1$ line, separated by a space. Each of $p,q$ is given to the 5th decimal place.
There is a newline at the end.

$0 \leq p \leq 1$
$0.1 \leq q \leq 1$
$|P_1 - P_2| \geq 10^{-5}$

Output

Output $YES$ or $NO$. Print a newline at the end.

Sample

Sample 1
Input
0.80000 0.50000
Output
YES

In this case, $P_1 = 0.1$ and $P_2 = 0.2$.

Sample 2
Input
0.60000 0.50000
Output
NO

In this case, $P_1 = 0.2$ and $P_2 = 0.15$.

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