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.

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

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 $(x_2, y_2)$.

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 |