codeforces820B Mister B and Angle in Polygon 2017-06-28 09:42 123人阅读 评论(0) 收藏

B. Mister B and Angle in Polygon

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

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".

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题目的意思是给出一个正n凸多边形，让你选择3个顶点所成角度尽可能接近给出的角度k

思路：我们选一个顶点把他和与他不相邻的点连线一定会把一个角（n-2）等分，枚举选择的角度与k比就好了

#include<iostream>
#include<cstdio>
#include<cmath>
#include<cstring>
#include<algorithm>
#include<string>
#include<queue>
#include<stack>
#include<map>
#include<set>
using namespace std;
#define LL long long
const int inf=0x3f3f3f3f;

int main()
{
    int n,x;
    scanf("%d%d",&n,&x);
    double p=180.0/n;
    double ans=inf;
    int cnt=-1;
    for(int i=1; i<=n-2; i++)
    {
        if(fabs(ans-x)-fabs(p*i-x)>1e-9)
            ans=p*i,cnt=i;
    }
    printf("%d %d %d\n",n-cnt,1,n);
    return 0;
}