Score : $600$ points

问题描述

我们有五种不同重量的包裹：$1$, $2$, $3$, $4$, $5$。对于每一种$i$ $(1 \leq i \leq 5)$，有$A_i$个重量为$i$的包裹。

另外，我们有五种不同力气的人：$1$, $2$, $3$, $4$, $5$。对于每一种$i$ $(1 \leq i \leq 5)$，有$B_i$个力气为$i$的人。

每个人可以携带任意数量的包裹（可能为零），但包裹总重量必须不超过其力气值。

你将获得$T$个测试用例。对于每个案例，请确定是否有可能通过适当分配包裹使人人都能携带所有包裹。也就是说，判断是否存在一种方法，将每个包裹分配给某个人，使得每个人都被分配到总重量不超过其力气值的包裹。允许有人不携带任何包裹。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

We have parcels with five different weights: $1$, $2$, $3$, $4$, $5$. For each $i$ $(1 \leq i \leq 5)$, there are $A_i$ parcels of weight $i$.
Additionally, we have people with five different strengths: $1$, $2$, $3$, $4$, $5$. For each $i$ $(1 \leq i \leq 5)$, there are $B_i$ people with strength $i$.
Each person can carry any number of parcels (possibly zero), but the total weight of the parcels must not exceed their strength.

You are given $T$ test cases. For each case, determine whether it is possible for the people to carry all parcels with the appropriate allocation of parcels. That is, determine whether it is possible to allocate each parcel to someone so that each person is allocated parcels whose total weight does not exceed their strength. It is fine to have someone who carries no parcels.

Constraints

• $1 \leq T \leq 5\times 10^4$
• $0 \leq A_i,B_i \leq 10^{16}$
• $1 \leq A_1+A_2+A_3+A_4+A_5$
• $1 \leq B_1+B_2+B_3+B_4+B_5$
• All values in input are integers.

Input

Input is given from Standard Input. The first line contains the number of test cases $T$:

$T$

Then, $T$ test cases follow, each in the following format:

$A_1$ $A_2$ $A_3$ $A_4$ $A_5$

$B_1$ $B_2$ $B_3$ $B_4$ $B_5$

Output

Print $T$ lines. The $i$-th line $(1\leq i\leq T)$ should contain Yes if all parcels can be carried in the $i$-th test case, and No otherwise.

Sample Input 1

3
5 1 0 0 1
0 0 0 2 1
0 3 0 0 0
0 0 2 0 0
10000000000000000 0 0 0 0
0 0 0 0 2000000000000000

Sample Output 1

Yes
No
Yes

In the first test case, all parcels can be carried. Here is one way to do so:

• The first person with strength $4$ carries four parcels of weight $1$.
• The second person with strength $4$ carries one parcel of weight $1$ and another of weight $2$.
• The person with strength $5$ carries one parcel of weight $5$.

In the second test case, one of the two people with strength $3$ has to carry two or more parcels of weight $2$, which is impossible.

update @ 2024/3/10 09:56:22