One beautiful day Vasily the bear painted 2m circles of the same radius R on a coordinate plane. Circles with numbers from 1 to m had centers at points (2R - R, 0), (4R - R, 0), ..., (2Rm - R, 0), respectively. Circles with numbers from m + 1 to 2m had centers at points (2R - R, 2R), (4R - R, 2R), ..., (2Rm - R, 2R), respectively. Naturally, the bear painted the circles for a simple experiment with a fly. The experiment continued for m 2 days. Each day of the experiment got its own unique number from 0 to m 2 - 1, inclusive. On the day number i the following things happened: The fly arrived at the coordinate plane at the center of the circle with number ( is the result of dividing number x by number y , rounded down to an integer). The fly went along the coordinate plane to the center of the circle number ( is the remainder after dividing number x by number y ). The bear noticed that the fly went from the center of circle v to the center of circle u along the shortest path with all points lying on the border or inside at least one of the 2m circles. After the fly reached the center of circle u , it flew away in an unknown direction. Help Vasily, count the average distance the fly went along the coordinate plane during each of these m 2 days.

输入描述:

The first line contains two integers m, R (1 ≤ m ≤ 105, 1 ≤ R ≤ 10).

输出描述:

In a single line print a single real number — the answer to the problem. The answer will be considered correct if its absolute or relative error doesn't exceed 10 - 6.

备注:

Figure to the second sample