CodeForces667APouring Rain

Description

A lot of people in Berland hates rain, but you do not. Rain pacifies, puts your thoughts in order. By these years you have developed a good tradition — when it rains, you go on the street and stay silent for a moment, contemplate all around you, enjoy freshness,
think about big deeds you have to do.

Today everything had changed quietly. You went on the street with a cup contained water, your favorite drink. In a moment when you were drinking a water you noticed that the process became quite long: the cup still contained water because of rain. You decided
to make a formal model of what was happening and to find if it was possible to drink all water in that situation.

Thus, your cup is a cylinder with diameter equals d centimeters. Initial level of water in cup equals h centimeters from the
bottom.



You drink a water with a speed equals v milliliters per second. But rain goes with such speed that if you do not drink a water from the cup, the level of water increases on e centimeters
per second. The process of drinking water from the cup and the addition of rain to the cup goes evenly and continuously.

Find the time needed to make the cup empty or find that it will never happen. It is guaranteed that if it is possible to drink all water, it will happen not later than after 104 seconds.

Note one milliliter equals to one cubic centimeter.

Input

The only line of the input contains four integer numbers d, h, v, e (1 ≤ d, h, v, e ≤ 104),
where:

d — the diameter of your cylindrical cup,
h — the initial level of water in the cup,
v — the speed of drinking process from the cup in milliliters per second,
e — the growth of water because of rain if you do not drink from the cup.

Output

If it is impossible to make the cup empty, print "NO" (without quotes).

Otherwise print "YES" (without quotes) in the first line. In the second line print a real number — time in seconds needed the cup will be empty. The answer will be considered correct if its relative or absolute error
doesn't exceed 10 - 4. It is guaranteed that if the answer exists, it doesn't exceed 104.

Sample Input

Input

1 2 3 100

Output

NO

Input

1 1 1 1

Output

YES
3.659792366325
题意：一个人喝一杯饮料，在他一边喝的同时雨水也在同时灌入（简直不敢想象），给出圆柱形杯的底面直径a，原有饮料的高度b，此人喝饮料的速度c(cm^3/s),以及当此人不喝饮料时雨水灌入升速（cm/s),判断此人能否将瓶中饮料喝完，如果能喝完，算出所用时长。
代码如下：
#include<stdio.h>
#include<math.h>
#define PI acos(0)*2
int main()
{
double a,b,c,d;
while(scanf("%lf%lf%lf%lf",&a,&b,&c,&d)!=EOF)
{
double r=a/2;
double V=PI*r*r*b;
double vrain=PI*r*r*d;
if(c<vrain)
printf("NO\n");
else
{
double t;
t=V/(c-vrain);
printf("YES\n%.12lf\n",t);
}
}
}