Snuke 密度 - المسألة

#15804. Snuke 密度

الإحصائيات

تم استخدام هذه المسألة في المسابقات التالية:

MIPT Training Camp 2015. Day 3. Makoto Soejima Contest 3

AI Translation — This statement was translated using AI and may contain inaccuracies. Please refer to the original statement if in doubt.

$c!$ 只 Snuke 正在一间大小为 $a! \times b!$ 的矩形房间里睡觉。请判断该房间的 Snuke 密度 $\frac{c!}{a!b!}$ 是否为整数。

输入格式

输入的第一行包含三个整数 $a$，$b$ 和 $c$。

数据范围

$1 \le a, b, c \le 10^{11}$

输出格式

如果 $\frac{c!}{a!b!}$ 是整数，输出 "YES"。否则，输出 "NO"。

样例

输入样例 1

2 3 4

输出样例 1

YES

输入样例 2

100000000000 100000000000 100000000000

输出样例 2

NO

说明

在样例 1 中，$\frac{4!}{2!3!} = 2$ 是一个整数。

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