#421(div2)B. Mister B and Angle in Polygon

Posted 2020-09-25 早知如此绊人心，何如当初莫相识。

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 (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 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 . If there are multiple optimal solutions, print any of them. The vertices are numbered from 1 to n in clockwise order.

Examples

Input

3 15

Output

1 2 3

Input

4 67

Output

2 1 3

Input

4 68

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".

题意：给出N,X,问正N边形，我们找出三个点，使其组成的角度最接近X，点的编号按照顺时针增加

思路：正多边形，我们可以知道三个点组成的角度只有N-2个，我们可以求出最小的那个角度即2 1 3，第二小的为2 1 4 ，最大的为  2  1  N

 1 #include<bits/stdc++.h>
 2 using namespace std;
 3 
 4 int main(){
 5    int n,x;
 6    cin>>n>>x;
 7    double sum=(n-2)*180*1.0;
 8    double s1=sum/n*1.0;
 9    int xx=n-2;
10    double  MMin=s1/xx*1.0;
11    double Min=1e9;
12    int k;
13    for(int i=1;i<=n-2;i++){
14         double y=abs(MMin*i-x)*1.0;
15         if(y<Min){
16             Min=y;
17             k=i;
18         }
19    }
20    cout<<2<<" "<<1<<" "<<2+k<<endl;
21 }