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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Collections;
using System.Linq;
namespace Atcoder_0404
{
    class Program
    {
        static void Main(string[] args)
        {
            var ABHM = GetInput_int();
            var a = ABHM[0];
            var b = ABHM[1];
            var hour = ABHM[2];
            var min = ABHM[3];
            var hourKaku = (hour / 12f )+(min  / (60f*12f));

            var minKaku = min / 60f;
            var targetKaku = Math.Abs(minKaku - hourKaku);
            if (targetKaku > 180) targetKaku = 360 - targetKaku;
            var cos = Math.Cos(targetKaku * Math.PI *2);
            var result2 = a*a + b*b - 2 * b*a * cos;
            var result = Math.Sqrt(result2);
            Console.WriteLine(result);
        }
        
        #region input
        

        static string[] GetInput_string()
        {
            var input = Console.ReadLine().Split(' ');
            return input;
        }

        static int[] GetInput_int()
        {
            var input = GetInput_string();
            var result = new int[input.Length];
            for (int i = 0; i < result.Length; i++)
            {
                result[i] = int.Parse(input[i]);
            }
            return result;
        }
        static long[] GetInput_long()
        {
            var input = GetInput_string();
            var result = new long[input.Length];
            for (int i = 0; i < result.Length; i++)
            {
                result[i] = long.Parse(input[i]);
            }
            return result;
        }
        #endregion
        #region sonota
        static void Swap_array<T>(T[] target, int a, int b)
        {
            T temp = target[a];
            target[a] = target[b];
            target[b] = temp;
        }
        static void Swap_list<T>(List<T> target, int a, int b)
        {
            T temp = target[a];
            target[a] = target[b];
            target[b] = temp;
        }
        /// <summary>
        /// 最大公約数
        /// </summary>
        public static int GCD(int a, int b)
        {

            /* 自然数 a > b を確認・入替 */
            if (a < b)
            {
                int tmp = a;
                a = b;
                b = tmp;
            }

            /* ユークリッドの互除法 */
            int r = a % b;
            while (r != 0)
            {
                a = b;
                b = r;
                r = a % b;
            }
            return b;
        }

        /// <summary>
        /// 最小公倍数
        /// </summary>
        public static int LCM(int a, int b)
        {
            int x = a * b;
            b = GCD(a, b);
            return x / b;

        }
        #endregion

        static long mod = 1000000000 + 7;
        
    }
}