eolymp
bolt
Попробуйте наш новый интерфейс для отправки задач

Wall

Лимит времени 1 секунда
Лимит использования памяти 64 MiB

Once upon a time there was a greedy King who ordered his chief Architect to build a wall around the King’s castle. The King was so greedy, that he would not listen to his Architect’s proposals to build a beautiful brick wall with a perfect shape and nice tall towers. Instead, he ordered to build the wall around the whole castle using the least amount of stone and labor, but demanded that the wall should not come closer to the castle than a certain distance. If the King finds that the Architect has used more resources to build the wall than it was absolutely necessary to satisfy those requirements, then the Architect will loose his head. Moreover, he demanded Architect to introduce at once a plan of the wall listing the exact amount of resources that are needed to build the wall.

Figure 1: Wall around the castle

Your task is to help poor Architect to save his head, by writing a program that will find the minimum possible length of the wall that he could build around the castle to satisfy King’s requirements.

The task is somewhat simplified by the fact, that the King’s castle has a polygonal shape and is situated on a flat ground. The Architect has already established a Cartesian coordinate system and has precisely measured the coordinates of all castle’s vertices in feet.

Входные данные

The input file consists of multiple data sets.

The first line of each data set contains two integer numbers N and L separated by a space. N (3N1000) is the number of vertices in the King’s castle, and L (1L1000) is the minimal number of feet that King allows for the wall to come close to the castle.

Next N lines describe coordinates of castle’s vertices in a clockwise order. The i-th line contains two integer numbers X_i and Y_i separated by a space (-10000X_i, Y_i10000) that represent the coordinates of the i-th vertex. All vertices are different and the sides of the castle do not intersect anywhere except for vertices.

The end of the input file is indicated by N = L = 0.

Выходные данные

For each case, write a line that contains the single number that represents the minimal possible length of the wall in feet that could be built around the castle to satisfy King’s requirements. You must present the integer number of feet to the King, because the floating numbers are not invented yet. However, you must round the result in such a way, that it is accurate to 8 inches (1 foot is equal to 12 inches), since the King will not tolerate larger error in the estimates.

Пример

Входные данные #1
9 100
200 400
300 400
300 300
400 300
400 400
500 400
500 200
350 200
200 200
0 0
Выходные данные #1
1628
Источник ACM International Collegiate Programming Contest, Summer Camp (2nd Day), Tokyo, 2005–9–24