No.218 1.5x Experience
タグ : / 解いたユーザー数 521
作問者 :
yuppe19 😺
Problem Statement
$P$ is playing a certain social game.
Suppose that $a$ experience points are required to upgrade a certain character to the maximum level.
One upgrade material increases the character's experience points by $b$.
From time to time, an event called the "$1.5$x Experience Campaign" is held,
and during this campaign, one upgrade material increases the experience points by $c$.
(There are cases where $c=1.5b$ does not hold.)
$P$ has formed a hypothesis:
キャンペーン期間中はレベル最大まで強化するのに必要な強化素材の数が、 通常期間に比べて $2/3$ の割合で足りるのではないか（つまり、$2/3$ 以下の個数で十分）That is the hypothesis.
Determine whether this hypothesis is correct.
Note that a single upgrade material cannot be split so that only the necessary portion is used (see Sample 2).
Input
$a$ $b$ $c$
$a$, $b$, $c$ are all positive integers.
$0 \lt a \lt 1,000,000$
$0 \lt b \lt c \lt 1,000,000$
Output
Print $\verb"YES"$ if $P$'s hypothesis is correct, and $\verb"NO"$ otherwise.
Print a newline after your answer.
Sample
Sample 1
Input
60000 10000 15000
Output
YES
Normally, the maximum level can be reached with $6$ materials.
During the campaign, it is possible with $4$, so the hypothesis is correct.
Sample 2
Input
50000 10000 15000
Output
NO
Normally, the maximum level can be reached with $5$ materials.
During the campaign, we get $50000 \div 15000 = 3.333...$, so $3$ materials are not enough.
You cannot use just $1/3$ of the $4$th material; a whole one is required.
Therefore, during the campaign the maximum level can be reached with $4$ materials,
and the $5 \times 2/3 = 10/3$ based on the hypothesis is not enough.
Sample 3
Input
63204 10538 15776
Output
NO
Normally, $6$ materials.
During the campaign... what! $4$ isn't enough?! Why?!
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