403196: GYM101064 C Cahokia ruins

Cahokia is the area of an ancient civilization located in the state of Illinois. This place importance comes from the fact that it helps understand the history of North America. Cahokia was composed by 120 mounds, 80 of them still remain nowadays. One of these mounds is called Monks Mound, considered the biggest natural monument in all North America.

Recently, a group of archaeologist of the organization Extraordinary Mystery Investigators (IME, in their language) have discovered secret passages in the underground surroundings of Monks Mound. Because of the importance of this discovery, IME has called one of its famous members, Marcio "the indispensable" Himura, for help. After diving in Thai seas, Marcio is back in action and want to unfold the mysteries of Cahokia. The members of IME want to reach the deepest part of Monk Mound, but to do so, they have to traverse a special room.

This room can be represented by a 2D grid with dimensions H × W meters. The particularity of this room is that the instant somebody enters the room the east and west walls begin to move towards each other until they collide. Marcio suspects that this was made to keep safely treasures from intruders. Each wall is represented by a sequence of H integers a₁, a₂, ..., a_H, where a_i is the width (in meters) of the wall at row i. Marcio knows that each wall moves with speed of 1 m / s. The following figure depicts (a) the initial configuration of the room given in the first sample test case, and (b) the collision of the walls after one second.

Marcio is interested in knowing, given an initial configuration of the walls, in how much time the walls collide after someone enter the room. This information is crucial for Marcio to determine an strategy to go through the room. He acknowledges your potential, so he ask for your help to solve this problem.

In the first line we give two space-separated integers, H (2 ≤ H ≤ 10⁵) and W (4 ≤ W ≤ 10⁵). In the second line, there are H space-separated integers representing the east wall. In the third line, there are H space separated-integers representing the west wall. It is ensured that the walls don't overlap at any row.

One number representing in how much time the two walls hit each other. Error of 10^- 9 is tolerated.

4 6
1 1 1 3
1 2 1 1

1

4 100
10 10 20 30
15 35 20 10

27.5