hrbeu1280Turn the corner

Description

Mr. West bought a new car! So he is travelling around the city.

One day he comes to a vertical corner. The street he is currently in has a width x, the street he wants to turn to has a width y. The car has a length l and a width d.

Can Mr. West go across the corner?

Input

Every line has four real numbers, x, y, l and w.

Proceed to the end of file.

Output

If he can go across the corner, print "yes". Print "no" otherwise.

Sample Input

10 6 13.5 4
10 6 14.5 4

Sample Output

yes
no

double Cal(double L)
{
	double s = l * cos(L) + w * sin(L) - x;
	double h = s * tan(L) + w * cos(L);
	return h;
}

#include <iostream>
#include <cstdio>
#include <cmath>
using namespace std;

#define PI 3.1415926535897932384626
const double EPS = 1e-10;
double x,y,l,w;

double Cal(double L)
{
	double s = l * cos(L) + w * sin(L) - x;
	double h = s * tan(L) + w * cos(L);
	return h;
}

double Solve(void)
{
	double Left, Right;
	double mid, midmid;
	double mid_value, midmid_value;
	Left = 0; Right = PI*0.5;
	while (Left + EPS < Right)
	{
		mid = (Left + Right) / 2;
		midmid = (mid + Right) / 2;
		mid_value = Cal(mid);
		midmid_value = Cal(midmid);
		if (mid_value >= midmid_value) Right = midmid;
		else Left = mid;
	}
	return Cal(Left);
}

int main()
{
	freopen("in.txt","r",stdin);
	while(cin>>x>>y>>l>>w)
	{
		if(x<w||y<w) cout<<"no"<<endl;
		else
		{
			double H = Solve();
			if(H>0&&H<y) cout<<"yes"<<endl;
			else cout<<"no"<<endl;
		}
	}
	return 0;
}