Problem:
Score: 300 points

Problem Statement

Consider an analog clock whose hour and minute hands are A and B centimeters long, respectively.

An endpoint of the hour hand and an endpoint of the minute hand are fixed at the same point, around which each hand rotates clockwise at constant angular velocity. It takes the hour and minute hands 12 hours and 1 hour to make one full rotation, respectively.

At 0 o'clock, the two hands overlap each other. H hours and M minutes later, what is the distance in centimeters between the unfixed endpoints of the hands?

Constraints

All values in input are integers.

1 \leq A, B \leq 1000

0 \leq H \leq 11

0 \leq M \leq 59

Input

Input is given from Standard Input in the following format:

A B H M

Output

Print the answer without units. Your output will be accepted when its absolute or relative error from the correct value is at most 10^{-9}.

Sample Input 1

3 4 9 0

Sample Output 1

5.00000000000000000000

The two hands will be in the positions shown in the figure below, so the answer is 5 centimeters.

Sample Input 2

3 4 10 40

Sample Output 2

4.56425719433005567605

The two hands will be in the positions shown in the figure below. Note that each hand always rotates at constant angular velocity.

Solution in Java (OpenJDK 11.0.6) (judge verdict: Runtime Error)

import java.math.BigDecimal;
import java.math.MathContext;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		// TODO 自動生成されたメソッド・スタブ
		Scanner in = new Scanner(System.in);
		String a = in.next();
		String b = in.next();
		String h = in.next();
		String m = in.next();

		BigDecimal a2 = new BigDecimal(a);
		BigDecimal b2 = new BigDecimal(b);
		BigDecimal hour = new BigDecimal(h);
		BigDecimal minute = new BigDecimal(m);

		BigDecimal x = new BigDecimal(360);
		BigDecimal y = new BigDecimal(60);
		BigDecimal z = new BigDecimal(12);
		BigDecimal v = new BigDecimal(180);

		BigDecimal long_needle = minute.multiply(x.divide(y));
		BigDecimal short_needle = (((hour.multiply(y)).add(minute))).multiply(x).divide(z.multiply(y));

		BigDecimal dif = BigDecimal.ZERO;
		BigDecimal rad = BigDecimal.ZERO;
		BigDecimal result = BigDecimal.ZERO;

		if((long_needle.compareTo(short_needle)) > 0) {
			/*if(l - s <= 90) {
				dif = l - s;
			}else if(l - s <= 180){
				dif = 90 - (l - s);
			}else if(l - s < 270){
				dif = 180 - (l - s);
			}else {
				dif = 360 - (l - s);
			}
			*/
			dif = long_needle.subtract(short_needle);
		}else {
			/*
			if(s - l <= 90) {
				dif = s - l;
			}else if(s - l <= 180){
				dif = 90 - (s - l);
			}else if(s - l < 270){
				dif = 180 - (s - l);
			}else {
				dif = 360 - (s - l);
			}
			*/
			dif = short_needle.subtract(long_needle);
		}
		BigDecimal p = new BigDecimal(Math.PI);
		rad = dif.multiply(p.multiply(v));

		String rad_kari = rad.toString();
		double r = Double.parseDouble(rad_kari);
		double cos = Math.cos(r);
		rad = new BigDecimal(cos);
		v = new BigDecimal(2);

		result = (a2.pow(2)).add(b2.pow(2)).subtract(v.multiply(a2.multiply(b2)).multiply(rad));
		result = sqrt(result,50);

		/*
		System.out.println(l);
		System.out.println(s);
		System.out.println(dif);
		*/
		System.out.println(String.format("%.20f", result));
	}

	public static BigDecimal sqrt(BigDecimal a, int scale){

        BigDecimal x = new BigDecimal(Math.sqrt(a.doubleValue()), MathContext.DECIMAL64);
        if(scale < 17){
             x = x.setScale(scale, BigDecimal.ROUND_HALF_EVEN);
             return x;
        }

        BigDecimal b2 = new BigDecimal(2);
        for(int tempScale = 16; tempScale < scale; tempScale *= 2){
            x = x.subtract(
                    x.multiply(x).subtract(a).divide(
                    x.multiply(b2), scale, BigDecimal.ROUND_HALF_EVEN));
        }
        return x;
    }

}