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.util.*;
import java.io.*;
class Main{
  public static void main(String args[]){
    int a = readI(),b = readI(),h=readI(),m=readI();
    h = 60*h+m;
    double rada = 0.5*h,radb = m*6.0;
    double rad = Math.abs(rada-radb);
    if(rad>180){rad=360-rad;}
    rad = rad*2*Math.PI/360;
    double k = Math.sqrt(a*a+b*b-2*a*b*Math.cos(rad));
    pl(k+"");
  }

  public static long search(int now,int n,int m,int x,long nowm,int[]rikai,int money[],int[][]book,long min){
    boolean flg=true;
    nowm+=money[now];
    for(int i=0;i<m;i++){
      rikai[i]+=book[now][i];
      if(rikai[i]<x){
        flg=false;
      }
    }
    if(flg){
      if(min==-1||min>nowm){
        min = nowm;
      }
    }else{
      for(int i=now+1;i<n;i++){
        min = search(i,n,m,x,nowm,rikai,money,book,min);
      }
    }
    for(int i=0;i<m;i++){
      rikai[i]-=book[now][i];
    }
    nowm-=money[now];
    if(now!=n-1){
      min = search(now+1,n,m,x,nowm,rikai,money,book,min);
    }
    return min;
  }

  static final BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
  public static void pr(String str){
    System.out.print(str);
  }
  public static void pl(String str){
    System.out.println(str);
  }
  public static String readL(){
    try{
      return br.readLine();
    }catch(IOException e){
      e.printStackTrace();
      return "";
    }
  }
  public static String readS(){
    StringBuilder sb = new StringBuilder();
    while(true){
      try{
        int k = br.read();
        if(k==-1||(char)k==' '||(char)k=='\n'){break;}
        sb.append((char)k);
      }catch(IOException e){
        e.printStackTrace();
      }
    }
    return sb.toString();
  }
  public static int readI(){
    return stoi(readS());
  }
  public static String[] readSs(){
    return readL().split(" ");
  }
  public static int[] readIs(){
    return stoi(readSs());
  }
  public static int stoi(String s){
    return Integer.parseInt(s);
  }
  public static int[] stoi(String s[]){
    int a[]=new int[s.length];
    for(int i=0;i<s.length;i++){
      a[i]=stoi(s[i]);
    }
    return a;
  }
  public static String itos(int i){
    return String.valueOf(i);
  }
  public static String[] itos(int[] a){
    String s[]=new String[a.length];
    for(int i=0;i<a.length;i++){
      s[i]=itos(a[i]);
    }
    return s;
  }
  public static String ctos(char c){
    return String.valueOf(c);
  }
  public static String cstos(char[] c){
    return new String(c);
  }
  public static char stoc(String s){
    return s.charAt(0);
  }
  public static char[] stocs(String s){
    return s.toCharArray();
  }
}