Exercising Walk

题意翻译

## 题目描述 给定一个矩形，左下角顶点坐标为$(x_1,y_1)$，右上角顶点坐标为$(x_2,y_2)$。现在有一个起点$(x,y)$,以及四个数$a,b,c,d$,问能否从起点开始走若干步（向左，向右，向上或向下），使向左、右、下、上分别**共**走了$a,b,c,d$步。 ## 输入格式 有$t$ 组测试数据，第一行输入一个整数$t$$(1\le t\le 10^3)$。 每组测试数据共两行，第一行输入四个整数$a,b,c,d$ $( 0 \le a,b,c,d \le 10^8 , a+b+c+d \ge 1)$。第二行输入六个整数$x,y,x_1,y_1,x_2,y_2$$(-10^8\le x_1\le x\le x_2\le 10^8,-10^8\le y_1\le y\le y_2\le 10^8)$。 ## 输出格式 对于每一组测试数据，输出一行Yes或No。

题目描述

Alice has a cute cat. To keep her cat fit, Alice wants to design an exercising walk for her cat! Initially, Alice's cat is located in a cell $ (x,y) $ of an infinite grid. According to Alice's theory, cat needs to move: - exactly $ a $ steps left: from $ (u,v) $ to $ (u-1,v) $ ; - exactly $ b $ steps right: from $ (u,v) $ to $ (u+1,v) $ ; - exactly $ c $ steps down: from $ (u,v) $ to $ (u,v-1) $ ; - exactly $ d $ steps up: from $ (u,v) $ to $ (u,v+1) $ . Note that the moves can be performed in an arbitrary order. For example, if the cat has to move $ 1 $ step left, $ 3 $ steps right and $ 2 $ steps down, then the walk right, down, left, right, right, down is valid. Alice, however, is worrying that her cat might get lost if it moves far away from her. So she hopes that her cat is always in the area $ [x_1,x_2]\times [y_1,y_2] $ , i.e. for every cat's position $ (u,v) $ of a walk $ x_1 \le u \le x_2 $ and $ y_1 \le v \le y_2 $ holds. Also, note that the cat can visit the same cell multiple times. Can you help Alice find out if there exists a walk satisfying her wishes? Formally, the walk should contain exactly $ a+b+c+d $ unit moves ( $ a $ to the left, $ b $ to the right, $ c $ to the down, $ d $ to the up). Alice can do the moves in any order. Her current position $ (u, v) $ should always satisfy the constraints: $ x_1 \le u \le x_2 $ , $ y_1 \le v \le y_2 $ . The staring point is $ (x, y) $ . You are required to answer $ t $ test cases independently.

输入输出格式

输入格式

The first line contains a single integer $ t $ ( $ 1 \le t \le 10^3 $ ) — the number of testcases. The first line of each test case contains four integers $ a $ , $ b $ , $ c $ , $ d $ ( $ 0 \le a,b,c,d \le 10^8 $ , $ a+b+c+d \ge 1 $ ). The second line of the test case contains six integers $ x $ , $ y $ , $ x_1 $ , $ y_1 $ , $ x_2 $ , $ y_2 $ ( $ -10^8 \le x_1\le x \le x_2 \le 10^8 $ , $ -10^8 \le y_1 \le y \le y_2 \le 10^8 $ ).

输出格式

For each test case, output "YES" in a separate line, if there exists a walk satisfying her wishes. Otherwise, output "NO" in a separate line. You can print each letter in any case (upper or lower).

输入输出样例

输入样例 #1

6
3 2 2 2
0 0 -2 -2 2 2
3 1 4 1
0 0 -1 -1 1 1
1 1 1 1
1 1 1 1 1 1
0 0 0 1
0 0 0 0 0 1
5 1 1 1
0 0 -100 -100 0 100
1 1 5 1
0 0 -100 -100 100 0

输出样例 #1

Yes
No
No
Yes
Yes
Yes

说明

In the first test case, one valid exercising walk is $ $(0,0)\rightarrow (-1,0) \rightarrow (-2,0)\rightarrow (-2,1) \rightarrow (-2,2)\rightarrow (-1,2)\rightarrow(0,2)\rightarrow (0,1)\rightarrow (0,0) \rightarrow (-1,0) $ $