2018 Rocky Mountain Regional Contest

Start

2018-11-03 16:00 UTC

2018 Rocky Mountain Regional Contest

End

2018-11-03 21:00 UTC
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Problem C
Forest for the Trees

You are playing hide-and-go-seek in a forest with Belle. The forest has one tree at each of the positive integer lattice points. That is, there is a tree at every point $(x,y)$ where $x$ and $y$ are both positive integers. You may consider each tree as a point. A logging company has cut down all of the trees in some axis-aligned rectangle, including those on the boundary of the rectangle.

You are standing at $(0,0)$ and Belle is standing at $(x_ b,y_ b)$. You can see Belle if and only if there is no tree blocking your line of sight to Belle. If there is a tree at $(x_ b,y_ b)$, Belle will make it easier for you to find her by standing on the side of the tree facing your location.

For example, suppose that Belle is standing at $(2,6)$. If the trees in the rectangle with corners at $(1,1)$ and $(5,4)$ are cut down (blue rectangle in figure), then you can see Belle. However, if the rectangle was at $(3,5)$ and $(5,7)$ (red rectangle in figure), then the tree at $(1,3)$ would be in the way.

\includegraphics[width=0.45\textwidth ]{trees.pdf}

Given the rectangle and Belle’s location, can you see her?

Input

The first line of input contains two integer $x_ b$ and $y_ b$ ($1 \leq x_ b,y_ b \leq 10^{12}$), which are the coordinates that Belle is standing on.

The second line of input contains four integers $x_1$, $y_1$, $x_2$ and $y_2$ ($1 \leq x_1 \leq x_2 \leq 10^{12}$ and $1 \leq y_1 \leq y_2 \leq 10^{12}$), which specify two opposite corners of the rectangle at $(x_1, y_1)$ and $(x_2, y_2)$.

Output

If you can see Belle, display Yes.

Otherwise, display No and the coordinates of the closest tree that is blocking your view.

Sample Input 1 Sample Output 1
2 6
1 1 5 4
Yes
Sample Input 2 Sample Output 2
2 6
3 5 5 7
No
1 3
Sample Input 3 Sample Output 3
830844890448 39710592053
821266 42860 402207107926 423171345006
No
402207964848 19223704203