Bridge Across Rough Terrain

The profile of the Ural Mountains is a polyline $(x_1, y_1), (x_2, y_2), \dots, (x_N, y_N)$ where $x_1 < x_2 < \dots < x_N$. The starting and ending points of the profile are at sea level, so $y_1 = y_N = 0$.

Two distinct points $A$ and $B$ lie on the mountain profile, and a road must be built between them. The road runs along the mountain slopes and a horizontal bridge. The length of the bridge must not exceed $L$. Both ends of the bridge lie on the profile. The road enters the bridge from one end and leaves from the other. The bridge may not contain any point strictly below the polyline, because no tunnels are built.

Possible bridge placements	An impossible bridge placement

The first line contains two integers $N$ and $L$, where $2 \le N \le 100\,000$ is the number of polyline vertices and $1 \le L \le 10^6$ is the maximum bridge length. The second line contains the coordinates of point $A$, and the third line contains the coordinates of point $B$. The next $N$ lines contain the vertices $(x_1, y_1), (x_2, y_2), \dots, (x_N, y_N)$ of the polyline.

All coordinates have absolute value at most $10^6$. It is guaranteed that $x_1 < x_2 < \dots < x_N$, $y_1 = y_N = 0$, and that $A$ and $B$ lie on the polyline. The points $A$ and $B$ are different.

Print the coordinates of the bridge ends on the first and second lines, with at least 5 digits after the decimal point. If several answers exist, print any of them.