Score : $500$ points

问题陈述

Takahashi位于一个$xy$-平面。最初，他位于点$(s _ x,s _ y)$，并希望到达点$(t _ x,t _ y)$。

在$xy$-平面上有一个矩形$R\coloneqq\lbrace(x,y)\mid a-0.5\leq x\leq b+0.5,c-0.5\leq y\leq d+0.5\rbrace$。考虑以下操作：

• 选择一个包含在矩形$R$内的格点$(x,y)$。Takahashi会瞬间移动到相对于点$(x,y)$的当前位置对称点。

确定他在重复上述操作0到$10^6$次（包括两端点）后是否能够到达点$(t _ x,t _ y)$。如果可能，构造一条使他到达点$(t _ x,t _ y)$的操作序列。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

Takahashi is on an $xy$-plane. Initially, he is at point $(s _ x,s _ y)$, and he wants to reach point $(t _ x,t _ y)$.

On the $xy$-plane is a rectangle $R\coloneqq\lbrace(x,y)\mid a-0.5\leq x\leq b+0.5,c-0.5\leq y\leq d+0.5\rbrace$. Consider the following operation:

• Choose a lattice point $(x,y)$ contained in the rectangle $R$. Takahashi teleports to the point symmetric to his current position with respect to point $(x,y)$.

Determine if he can reach point $(t _ x,t _ y)$ after repeating the operation above between $0$ and $10^6$ times, inclusive. If it is possible, construct a sequence of operations that leads him to point $(t _ x,t _ y)$.

Constraints

• $0\leq s _ x,s _ y,t _ x,t _ y\leq2\times10^5$
• $0\leq a\leq b\leq2\times10^5$
• $0\leq c\leq d\leq2\times10^5$
• All values in the input are integers.

Input

The input is given from Standard Input in the following format:

$s _ x$ $s _ y$

$t _ x$ $t _ y$

$a$ $b$ $c$ $d$

Output

In the first line, print Yes if Takahashi can reach point $(t _ x,t _ y)$ after repeating the operation between $0$ and $10^6$ times, inclusive, and No otherwise. If and only if you print Yes in the first line, print $d$ more lines, where $d$ is the length of the sequence of operations you have constructed ($d$ must satisfy $0\leq d\leq10^6$). The $(1+i)$-th line $(1\leq i\leq d)$ should contain the space-separated coordinates of the point $(x, y)\in R$, in this order, that is chosen in the $i$-th operation.

Sample Input 1

1 2
7 8
7 9 0 3

Sample Output 1

Yes
7 0
9 3
7 1
8 1

For example, the following choices lead him from $(1,2)$ to $(7,8)$.

• Choose $(7,0)$. Takahashi moves to $(13,-2)$.
• Choose $(9,3)$. Takahashi moves to $(5,8)$.
• Choose $(7,1)$. Takahashi moves to $(9,-6)$.
• Choose $(8,1)$. Takahashi moves to $(7,8)$.

Any output that satisfies the conditions is accepted; for example, printing

Yes
7 3
9 0
7 2
9 1
8 1

is also accepted.

Sample Input 2

0 0
8 4
5 5 0 0

Sample Output 2

No

No sequence of operations leads him to point $(8,4)$.

Sample Input 3

1 4
1 4
100 200 300 400

Sample Output 3

Yes

Takahashi may already be at the destination in the beginning.

Sample Input 4

22 2
16 7
14 30 11 14

Sample Output 4

No

update @ 2024/3/10 12:05:14