Mister B and Angle in Polygon

2000ms

262144K

Description:

On one quiet day all of sudden Mister B decided to draw angle a on his field. Aliens have already visited his field and left many different geometric figures on it. One of the figures is regular convex n-gon (regular convex polygon with n sides).

That's why Mister B decided to use this polygon. Now Mister B must find three distinct vertices v₁, v₂, v₃ such that the angle $\text{[math]}$ (where v₂ is the vertex of the angle, and v₁ and v₃ lie on its sides) is as close as possible to a. In other words, the value $\text{[math]}$ should be minimum possible.

If there are many optimal solutions, Mister B should be satisfied with any of them.

Input:

First and only line contains two space-separated integers n and a (3 ≤ n ≤ 10⁵, 1 ≤ a ≤ 180) — the number of vertices in the polygon and the needed angle, in degrees.

Output:

Print three space-separated integers: the vertices v₁, v₂, v₃, which form $\text{[math]}$ . If there are multiple optimal solutions, print any of them. The vertices are numbered from 1 to n in clockwise order.

Sample Input:

3 15

Sample Output:

1 2 3

Sample Input:

4 67

Sample Output:

2 1 3

Sample Input:

4 68

Sample Output:

4 1 2

Note:

In first sample test vertices of regular triangle can create only angle of 60 degrees, that's why every possible angle is correct.

Vertices of square can create 45 or 90 degrees angles only. That's why in second sample test the angle of 45 degrees was chosen, since |45 - 67| < |90 - 67|. Other correct answers are: "3 1 2", "3 2 4", "4 2 3", "4 3 1", "1 3 4", "1 4 2", "2 4 1", "4 1 3", "3 1 4", "3 4 2", "2 4 3", "2 3 1", "1 3 2", "1 2 4", "4 2 1".

In third sample test, on the contrary, the angle of 90 degrees was chosen, since |90 - 68| < |45 - 68|. Other correct answers are: "2 1 4", "3 2 1", "1 2 3", "4 3 2", "2 3 4", "1 4 3", "3 4 1".

Informação

Provedor Codeforces

Código CF820B