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# (Mono-csc 3.5.0) (judge verdict: Wrong Answer)

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

namespace PaizaTest
{
    class Program
    {
        static void Main(string[] args)
        {

            var ABHM = Console.ReadLine().Split().Select(double.Parse).ToList();

            double result = 0.0;

            if (ABHM[2] % 3 == 0 && ABHM[3] == 0)
            {
                result = Math.Sqrt(ABHM[0] * ABHM[0] + ABHM[1] * ABHM[1]);
            }
            else
            {
                // 時針は1hにつき30°動く1mで0.5°動く
                double hourRad = (double)(ABHM[2] * 30.0 + ABHM[3] * 0.5);
                //double hourRad = (double)(ABHM[2] * 30.0);
                // 分針は1mにつき6°動く
                double minRad = (double)(ABHM[3] * 6.0);
                // 角度を求めた後、内側の角度を求める
                // 大きい方から小さい方を引く
                double diff = Math.Abs(Math.Max(hourRad, minRad) - Math.Min(hourRad, minRad));
                bool isReverse = false;
                // 差が180より大きい場合、360°から引く
                if (diff > 180.0)
                {
                    diff = 360.0 - diff;
                    isReverse = true;
                }
                double diffValue = double.MaxValue;
                int matchRad = 0;
                // 求めた角度で片方をループ変数にしてループ
                for (int i = 0; i <= diff; i++)
                {
                    var hourLen = ABHM[0] * Math.Cos((Math.PI * (double)i) / 180.0);
                    var minLen = ABHM[1] * Math.Cos(Math.PI * ((double)(diff - i)) / 180.0);

                    var radDiff = Math.Abs(hourLen - minLen);
                    if (diffValue > radDiff)
                    {
                        diffValue = radDiff;
                        matchRad = i;
                    }
                }
                // 最小値の角度でお互いのsinを計算
                var hourResult = ABHM[0] * Math.Sin((Math.PI * (double)matchRad) / 180.0);
                var minResult = ABHM[1] * Math.Sin((Math.PI * (double)(diff - matchRad)) / 180.0);
                result = hourResult + minResult;
            }

            Console.WriteLine(result);



#if DEBUG
            Console.ReadLine();
#endif
        }
    }
}