The Great Hero

题意翻译

### 题意 我们定义一个人物为一个二元组$(x, y)$, 称其中 $x$ 为攻击力, $y$ 为血量. 一个英雄是一个人物. 现在有 $n$ 个怪物, 每个怪物是一个人物. 我们这样定义两个人物 $A$ 与 $B$ 交战: - $A$ 的血量减少等同于 $B$ 的攻击力的数值, $B$ 的血量也减少等同于 $A$ 的攻击力的数值. - 然后, $A$ 和 $B$ 中所有血量小于等于 $0$ 的人物死亡. 现在英雄需要消灭所有怪物, 消灭怪物的方式是与之交战. 请求出英雄能不能消灭所有的怪物, 即使英雄本人在消灭所有怪物后死亡. ### 输入格式 第一行包含一个正整数 $T (1\leq T \leq 10^5)$, 表示有 $T$ 组测试数据. 接下来第 $3k-2$ 行, 包括第 $k$ 组数据中, 英雄的攻击力 $A (1\leq A\leq 10^6)$, 血量 $B (1\leq B\leq 10^6)$, 怪物个数 $n(1\leq n\leq 10^5)$. 接下来第 $3k-1$ 行, 包括对于每个 $i\in[1, n]$ 第 $k$ 组数据中第 $i$ 个怪物的攻击力 $a_i (1\leq a_i\leq 10^6)$. 接下来第 $3k$ 行, 包括对于每个 $i\in[1, n]$ 第 $k$ 组数据中第 $i$ 个怪物的血量 $b_i (1\leq b_i\leq 10^6)$. 所有数据的 $n$ 的总和小于等于 $10^5$. ### 输出格式 对于每组测试数据, 输出仅一行一个字符串 "YES"(如果英雄能够杀死所有怪物) 或 "NO"(如果英雄不能杀死所有怪物) (不包括括号).

题目描述

The great hero guards the country where Homer lives. The hero has attack power $ A $ and initial health value $ B $ . There are $ n $ monsters in front of the hero. The $ i $ -th monster has attack power $ a_i $ and initial health value $ b_i $ . The hero or a monster is said to be living, if his or its health value is positive (greater than or equal to $ 1 $ ); and he or it is said to be dead, if his or its health value is non-positive (less than or equal to $ 0 $ ). In order to protect people in the country, the hero will fight with monsters until either the hero is dead or all the monsters are dead. - In each fight, the hero can select an arbitrary living monster and fight with it. Suppose the $ i $ -th monster is selected, and the health values of the hero and the $ i $ -th monster are $ x $ and $ y $ before the fight, respectively. After the fight, the health values of the hero and the $ i $ -th monster become $ x-a_i $ and $ y-A $ , respectively. Note that the hero can fight the same monster more than once. For the safety of the people in the country, please tell them whether the great hero can kill all the monsters (even if the great hero himself is dead after killing the last monster).

输入输出格式

输入格式

Each test contains multiple test cases. The first line contains $ t $ ( $ 1 \le t \le 10^5 $ ) — the number of test cases. Description of the test cases follows. The first line of each test case contains three integers $ A $ ( $ 1 \leq A \leq 10^6 $ ), $ B $ ( $ 1 \leq B \leq 10^6 $ ) and $ n $ ( $ 1 \leq n \leq 10^5 $ ) — the attack power of the great hero, the initial health value of the great hero, and the number of monsters. The second line of each test case contains $ n $ integers $ a_1, a_2, \dots, a_n $ ( $ 1 \leq a_i \leq 10^6 $ ), where $ a_i $ denotes the attack power of the $ i $ -th monster. The third line of each test case contains $ n $ integers $ b_1, b_2, \dots, b_n $ ( $ 1 \leq b_i \leq 10^6 $ ), where $ b_i $ denotes the initial health value of the $ i $ -th monster. It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 10^5 $ .

输出格式

For each test case print the answer: "YES" (without quotes) if the great hero can kill all the monsters. Otherwise, print "NO" (without quotes).

输入输出样例

输入样例 #1

5
3 17 1
2
16
10 999 3
10 20 30
100 50 30
1000 1000 4
200 300 400 500
1000 1000 1000 1000
999 999 1
1000
1000
999 999 1
1000000
999

输出样例 #1

YES
YES
YES
NO
YES

说明

In the first example: There will be $ 6 $ fights between the hero and the only monster. After that, the monster is dead and the health value of the hero becomes $ 17 - 6 \times 2 = 5 > 0 $ . So the answer is "YES", and moreover, the hero is still living. In the second example: After all monsters are dead, the health value of the hero will become $ 709 $ , regardless of the order of all fights. So the answer is "YES". In the third example: A possible order is to fight with the $ 1 $ -st, $ 2 $ -nd, $ 3 $ -rd and $ 4 $ -th monsters. After all fights, the health value of the hero becomes $ -400 $ . Unfortunately, the hero is dead, but all monsters are also dead. So the answer is "YES". In the fourth example: The hero becomes dead but the monster is still living with health value $ 1000 - 999 = 1 $ . So the answer is "NO".