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: Accepted)

import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;
import java.io.*;
public class Main {
InputStream is;
	PrintWriter out;
	String INPUT = ""; 
//class  Declaration

static class pair implements Comparable<pair>{
	int x;
	int y;

	
	pair (int i,int j)
	{ x=i; y=j;
	
		
	}
	public int compareTo(pair p){
		if(this.x!=p.x) { return this.x-p.x;}
		else { return this.y-p.y;}
	}
	public int hashCode() { return (x+" "+y).hashCode();}
	public String toString(){ return x+" "+y;} 
	public boolean equals(Object o){ 
		pair x = (pair) o ;
		return (x.x==this.x&&x.y==this.y);}
}



long mod  = (long)1e9 + 7 ;
int inf = (int)1e9 +5  ; 
void solve() throws Exception{
	int[] a = na(4);
	// pn(0.5*(a[2]*60.0 + a[3]));
	// pn(6.0*a[3]);
	double angle =(0.5*(a[2]*60.0 + a[3])) - 6.0*a[3] ;
	angle = Math.min(angle,360.0-angle);
	//pn("angle "+angle);
	double ans = Math.sqrt(a[0]*a[0]*1.0 + a[1]*a[1]*1.0  - 2.0* a[1]*a[0]* Math.cos(Math.toRadians(angle))) ; 
	System.out.printf("%.13f\n",ans);
	
}



long pow(long a,long b){
	long result = 1;
	while(b>0){
	if(b%2==1) result = (result * a) % mod;
		b/=2;
		a=(a*a)%mod;
	}
	return result;
}

void print(Object o){
System.out.println(o);
System.out.flush();
}

int gcd(int a, int b) 
{ 
if (b == 0) 
return a; 
return gcd(b, a % b);  
}
void run() throws Exception{
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
}
	
	
public static void main(String[] args) throws Exception { new Main().run(); }
	
//output methods
private void pn(Object o)
{
	out.println(o);
}
private void p(Object o)
{
	out.print(o);
}



//input methods
		private byte[] inbuf = new byte[1024];
	public int lenbuf = 0, ptrbuf = 0;
	

	private int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	
	
	
	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }
	
	private String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
		
	private char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private void tr(Object... o) { if(INPUT.length() > 0)System.out.println(Arrays.deepToString(o)); }
	void watch(Object ... a) throws Exception{
		int i=1;
		print("watch starts :");
		for(Object o : a ) {
			//print(o);
			boolean notfound = true;
			if(o.getClass().isArray()){
				
				String type = o.getClass().getName().toString();
				//print("type is "+type);
				switch (type) {
					case "[I":{
						int[] test = (int[])o ;
						print(i+" "+Arrays.toString(test));
						break;
					}
					case "[[I":{
						int[][] obj = (int[][])o;
						
						print(i+" "+Arrays.deepToString(obj));
						break;
					}
					case "[J" : {
						
						long[] obj  = (long[])o ;
						print(i+" "+Arrays.toString(obj));
						break;
					}
					case "[[J": {
						
						long[][] obj = (long[][])o;
						print(i+" "+Arrays.deepToString(obj));
						break;
					}
					case "[D" :{
						
						double[] obj= (double[])o;
						print(i+" "+Arrays.toString(obj));
						break;
					}
					case "[[D" :{
						
						double[][] obj = (double[][])o;
						print(i+" "+Arrays.deepToString(obj));
						break;
					}
					case "[Ljava.lang.String": {
						
						String[] obj = (String[])o ;
						print(i+" "+Arrays.toString(obj));
						break;
					}
					case "[[Ljava.lang.String": {
						
						String[][] obj = (String[][])o ;
						print(i+" "+Arrays.deepToString(obj));
						break ; 
					}
					case "[C" :{
						char[] obj = (char[])o ;
						print(i+" "+Arrays.toString(obj));
						break;
					}
					case "[[C" :{
						
						char[][] obj = (char[][])o;
						print(i+" "+Arrays.deepToString(obj));
						break;
					}

						
				
					default:{
						print(i+" type not identified");
						break;
					}
				}
				notfound = false;
				
			}
			if(o.getClass() == ArrayList.class){
				print(i+" al: "+o);
				notfound = false;
			}
			if(o.getClass() == HashSet.class){
				print(i+" hs: "+o);
				notfound = false;
			}
			if(o.getClass() == TreeSet.class){
				print(i+" ts: "+o);
				notfound = false;
			}
			if(o.getClass() == TreeMap.class){
				print(i+" tm: "+o);
				notfound = false;
			}
			if(o.getClass() == HashMap.class){
				print(i+" hm: "+o);
				notfound = false;
			}
			if(o.getClass() == LinkedList.class){
				print(i+" ll: "+o);
				notfound = false;
			}
			if(o.getClass() == PriorityQueue.class){
				print(i+" pq : "+o);
				notfound = false;
			}
			if(o.getClass() == pair.class){
				print(i+" pq : "+o);
				notfound = false;
			}
			
			if(notfound){
				print(i+" unknown: "+o);
			}
			i++;
		}
		print("watch ends ");
	}

}