CF1480B.The Great Hero

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).

伟大的英雄守卫着荷马居住的国家。英雄的攻击力为 $A$，初始生命值为 $B$。英雄面前有 $n$ 只怪物，其中第 $i$ 只怪物的攻击力为 $a_i$，初始生命值为 $b_i$。

若某角色（英雄或怪物）的生命值为正（即 $\geq 1$），则称其为存活；若其生命值为非正（即 $\leq 0$），则称其为死亡。

为了保护国内百姓，英雄将持续与怪物战斗，直至英雄死亡，或所有怪物全部死亡。

• 每次战斗中，英雄可任选一只存活的怪物进行战斗。假设选择的是第 $i$ 只怪物，且战斗前英雄与该怪物的生命值分别为 $x$ 和 $y$，则战斗后英雄与该怪物的生命值分别变为 $x-a_i$ 和 $y-A$。

注意：英雄可以多次与同一只怪物战斗。

为保障国内百姓的安全，请告知他们：这位伟大的英雄是否能够消灭所有怪物（即使英雄在击杀最后一只怪物后随即死亡）。

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 $10^5$.

每个测试包含多个测试用例。第一行包含一个整数 $t$（$1 \le t \le 10^5$），表示测试用例的数量。随后是各测试用例的描述。

每个测试用例的第一行包含三个整数 $A$（$1 \leq A \leq 10^6$）、$B$（$1 \leq B \leq 10^6$）和 $n$（$1 \leq n \leq 10^5$），分别表示大英雄的攻击力、初始生命值以及怪物的数量。

每个测试用例的第二行包含 $n$ 个整数 $a_1, a_2, \dots, a_n$（$1 \leq a_i \leq 10^6$），其中 $a_i$ 表示第 $i$ 个怪物的攻击力。

每个测试用例的第三行包含 $n$ 个整数 $b_1, b_2, \dots, b_n$（$1 \leq b_i \leq 10^6$），其中 $b_i$ 表示第 $i$ 个怪物的初始生命值。

保证所有测试用例中 $n$ 的总和不超过 $10^5$。

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

对于每个测试用例，请输出答案：如果大英雄能够杀死所有怪物，则输出 "YES"（不带引号）；否则，输出 "NO"（不带引号）。

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 $17 - 6 \times 2 = 5 \gt 0$. 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".

第一个样例：英雄与唯一一个怪物将进行 $6$ 次战斗。战斗结束后，该怪物死亡，英雄的生命值变为 $17 - 6 \times 2 = 5 \gt 0$。因此答案为“YES”，且英雄仍然存活。

第二个样例：无论战斗顺序如何，当所有怪物均被击败后，英雄的生命值均为 $709$。因此答案为“YES”。

第三个样例：一种可行的战斗顺序是依次与第 $1$、第 $2$、第 $3$ 和第 $4$ 个怪物战斗。所有战斗结束后，英雄的生命值变为 $-400$。不幸的是，英雄已死亡，但所有怪物也均已死亡。因此答案为“YES”。

第四个样例：英雄死亡，而怪物仍存活，其生命值为 $1000 - 999 = 1$。因此答案为“NO”。