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 C# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;

namespace ForATCODER
{
    public class Program
    {
        ///template
        ///
        /// String[] s = Console.ReadLine().Split(' ');
        ///   long[] nk =  s2larray(Console.ReadLine().Split(' '));
        ///   

        public static void Main(string[] args)
        {
            //    String[] s = Console.ReadLine().Split(' ');
            long[] dat = s2larray(Console.ReadLine().Split(' '));
            double deg_h;
            double deg_m;
            deg_h = dat[2] * (360.0d/12.0d);
            deg_m = dat[3] * (360.0d / 60.0d);
            deg_h += dat[3] * 0.5;
            double degs = Math.Abs(deg_h - deg_m);
          //  if (degs > 180) degs -= 180d;
            //      double result = (dat[0] / (double)dat[1]) * Math.Tan(degs * Math.PI/180);
            double result = Math.Pow(dat[0],2) + Math.Pow(dat[1], 2)-2d*(dat[0]*dat[1]*1.0d)*Math.Cos(degs * Math.PI / 180.0d) ;
            result = Math.Sqrt(result);
            RESULT(result);


        }
        static void addarray(long[] arr ,int start,int end)
        {
            for(int i = start; i <= end;i++)
            {
                arr[i]++;
            }
        }
        public static decimal Sqrt(decimal x)
        {
            decimal sqrt_x = (decimal)Math.Sqrt((long)x);
            for (int i = 0; i < 10; ++i)
                sqrt_x = 0.5m * (sqrt_x + x / sqrt_x);
            return sqrt_x;
        }
        static   long summ(long s)
        {
            if (s == 1) return 1;
            return s + summ(s-1);
        }
        public static bool checka(int[] a, int m)
        {
            int back = 1;
            for (int i = 0; i < a.Length; i++)
            {
                if (a[i] >= 1 && a[i] <= m)
                {
                    if (a[i] >= back)
                    {
                        back = a[i];
                    }
                    else
                    {
                        return false;
                    }
                }
                else
                {
                    return false;
                }
            }
            return true;
        }
        public static ulong pow(int a, int b)
        {
            ulong res = 1;
            for (int i = 0; i < b; i++)
            {
                res *= (ulong)a;
            }
            return res;
        }
        static int s2i(String s)
        {
            return Convert.ToInt32(s);
        }
        static long s2l(String s)
        {
            return Convert.ToInt64(s);
        }
        static void RESULT(double res)
        {
            Console.WriteLine(res);
        }
        static void RESULT(long res)
        {
            Console.WriteLine(res);
        }
        static void RESULT(ulong res)
        {
            Console.WriteLine(res);
        }
        static void RESULT(int res)
        {
            Console.WriteLine(res);
        }
        static void RESULT(String res)
        {
            Console.WriteLine(res);
        }
        static String[] ReadLineAll(int count)
        {
            String[] res = new String[count];
            for (int i = 0; i < count; i++)
            {
                res[i] = Console.ReadLine();
            }
            return res;
        }

        static int[] s2iarray(String[] src)
        {
            int len = src.Length;
            int[] res = new int[len];
            for (int i = 0; i < len; i++)
            {
                res[i] = Convert.ToInt32(src[i]);
            }
            return res;
        }
        static long[] s2larray(String[] src)
        {
            int len = src.Length;
            long[] res = new long[len];
            for (int i = 0; i < len; i++)
            {
                res[i] = Convert.ToInt64(src[i]);
            }
            return res;
        }
        static ulong[] s2larray2(String[] src)
        {
            int len = src.Length;
            ulong[] res = new ulong[len];
            for (int i = 0; i < len; i++)
            {
                res[i] = Convert.ToUInt64(src[i]);
            }
            return res;
        }

        static long C(int n, int r)
        {
            if (n <= 1) return 0;
            if (r > n - r) r = n - r; // because C(n, r) == C(n, n - r)
            long ans = 1;
            int i;

            for (i = 1; i <= r; i++)
            {
                ans *= n - r + i;
                ans /= i;
            }

            return ans;
        }
        static long C(long n, long r)
        {
            if (n <= 1) return 0;
            if (r > n - r) r = n - r; // because C(n, r) == C(n, n - r)
            long ans = 1;
            int i;

            for (i = 1; i <= r; i++)
            {
                ans *= n - r + i;
                ans /= i;
            }

            return ans;
        }
        static ulong C(ulong n, ulong r)
        {
            if (n <= 1) return 0;
            if (r > n - r) r = n - r; // because C(n, r) == C(n, n - r)
            ulong ans = 1;
            ulong i;

            for (i = 1; i <= r; i++)
            {
                ans *= n - r + i;
                ans /= i;
            }

            return ans;
        }
    }

}