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: Accepted)

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

namespace Contest
{
  class Program
  {
    static void Main(string[] args)
    {
      ABC168.C();
    }
    class ABC168
    {
      public static void A()
      {
        var N = Read.Int();
        switch (N % 10)
        {
          case 0:
          case 1:
          case 6:
          case 8:
            Console.WriteLine("pon");return;
          case 3:
            Console.WriteLine("bon");return;
          case 2:
          case 4:
          case 5:
          case 7:
          case 9:
            Console.WriteLine("hon");return;
        }
      }
      public static void B()
      {
        var K = Read.Int();
        var S = Read.Str();
        Console.WriteLine(S.Length <= K ? S : S.Substring(0, K) + "...");
      }
      public static void C()
      {
        var A = Read.Int();
        var B = Read.Int();
        var H = Read.Int();
        var M = Read.Int();
        var r1 = Math.PI * (H * 60 + M) / 360;
        var r2 = Math.PI * M / 30;
        var x1 = Math.Cos(r1) * A;
        var y1 = Math.Sin(r1) * A;
        var x2 = Math.Cos(r2) * B;
        var y2 = Math.Sin(r2) * B;
        Console.WriteLine(Math.Sqrt(Math.Max(0, (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2))));
      }
      public static void D()
      {
        var N = Read.Int();
        var M = Read.Int();
        var Adj = Read.AdjacencyList(N, M);
        var ans = Enumerable.Range(0, N + 1).Select(i => -1).ToArray();
        var queue = new Queue<int>();
        queue.Enqueue(1);
        while (queue.Count > 0)
        {
          var v = queue.Dequeue();
          foreach(var w in Adj[v])
          {
            if (ans[w] >= 0) { continue; }
            ans[w] = v;
            queue.Enqueue(w);
          }
        }
        if (ans.Skip(2).Count(x => x < 0) > 0) { Console.WriteLine("No"); return; }
        Console.WriteLine("Yes");
        Console.WriteLine(String.Join(Environment.NewLine, ans.Skip(2)));
      }
      public static void E()
      {
        var N = Read.Int();
        var AB = Read.TupleLong(N);
        var Zero = new List<Tuple<long, long>>();
        var D1 = new List<Tuple<long, long>>();
        var D2 = new List<Tuple<long, long>>();

        var count1 = new Dictionary<long, Dictionary<long, long>>();
        var count2 = new Dictionary<long, Dictionary<long, long>>();

        foreach (var t in AB)
        {
          var X = t.Item1;
          var Y = t.Item2;
          if (X == 0 && Y == 0) { Zero.Add(new Tuple<long, long>(0, 0)); continue; }
          if (Y < 0)
          {
            X *= -1;
            Y *= -1;
          }
          var gcd = Util.GCD(Math.Abs(X), Y);
          X /= gcd;
          Y /= gcd;
          if (X >= 0)
          {
            if (!count1.ContainsKey(X)) { count1.Add(X, new Dictionary<long, long>()); }
            if (!count1[X].ContainsKey(Y)) { count1[X].Add(Y, 0); }
            count1[X][Y]++;
          }
          else
          {
            if (!count2.ContainsKey(X)) { count2.Add(X, new Dictionary<long, long>()); }
            if (!count2[X].ContainsKey(Y)) { count2[X].Add(Y, 0); }
            count2[X][Y]++;
          }
        }

        MOD two = 2;
        MOD ans = 1;
        foreach(var kvp1 in count1)
        {
          foreach(var kvp2 in kvp1.Value)
          {
            var X = kvp1.Key;
            var Y = kvp2.Key;
            var C = kvp2.Value;
            if (count2.ContainsKey(-Y) && count2[-Y].ContainsKey(X))
            {
              var C2 = count2[-Y][X];
              count2[-Y][X] = 0;
              ans = ans * (two.Power(C) + two.Power(C2) - 1);
            }
            else
            {
              ans = ans * (two.Power(C) - 0);
            }
          }
        }
        foreach (var kvp1 in count2)
        {
          foreach (var kvp2 in kvp1.Value)
          {
            ans = ans * two.Power(kvp2.Value);
          }
        }
        Console.WriteLine((ans + Zero.Count - 1).V);
      }
      public static void F()
      {

      }
    }


    class Util
    {
      public static long[] ASum(long[] array)
      {
        var res = new long[array.Length + 1];
        for (int i = 0; i < array.Length; ++i)
        {
          res[i + 1] = res[i] + array[i];
        }
        return res;
      }
      public static Dictionary<T, long> Frequency<T>(T[] array)
      {
        var dict = new Dictionary<T, long>();
        foreach (var a in array)
        {
          if (!dict.ContainsKey(a)) { dict.Add(a, 0); }
          dict[a]++;
        }
        return dict;
      }
      public static long GCD(long a, long b)
      {
        while (b > 0)
        {
          var c = a % b;
          a = b;
          b = c;
        }
        return a;
      }
    }
    struct MOD
    {
      public static long P = 1000000007;
      public readonly long V;

      public MOD(long a) { this.V = a % P; }
      public static implicit operator MOD(long a) { return new MOD(a); }
      public static MOD operator +(MOD a, MOD b) { return new MOD((a.V + b.V) % P); }
      public static MOD operator -(MOD a, MOD b) { return new MOD((a.V - b.V + P) % P); }
      public static MOD operator *(MOD a, MOD b) { return new MOD((a.V * b.V) % P); }
      public static MOD operator /(MOD a, MOD b) { return new MOD((a.V * b.Inverse().V) % P); }
      public MOD Inverse()
      {
        long a = V, p = P; long b = p, c = 1, d = 0, e = 0, f = 0;
        while (b != 0) { e = a / b; f = b; b = a - e * b; a = f; f = d; d = c - e * d; c = f; }
        c %= p;
        return c + (c < 0 ? p : 0);
      }
      public MOD Power(long n)
      {
        long a = V, p = P; long res = 1; long mult = a;
        for (int i = 0; i < 63; ++i) { if ((n & ((long)1 << i)) > 0) { res = (res * mult) % p; } mult = (mult * mult) % p; }
        return res;
      }
      public override string ToString() { return V.ToString(); }
    }


    static class Read
{
static Queue<string> queue = new Queue<string>();
static void Enqueue() { var ss = Console.ReadLine().Split(' '); foreach (var s in ss) { queue.Enqueue(s); } }
public static int Int() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt32(queue.Dequeue()); }
public static long Long() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt64(queue.Dequeue()); }
public static string Str() { if (queue.Count == 0) { Enqueue(); } return queue.Dequeue(); }
public static int[] IntN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt32(s)).ToArray(); }
public static long[] LongN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt64(s)).ToArray(); }
public static ulong[] ULongN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToUInt64(s)).ToArray(); }
public static string[] StrN() { return Console.ReadLine().Split(' '); }
public static Tuple<int, int>[] TupleInt(int n) { List<Tuple<int, int>> list = new List<Tuple<int, int>>(); for (int i = 0; i < n; ++i) { var ab = Read.IntN(); list.Add(new Tuple<int, int>(ab[0], ab[1])); } return list.ToArray(); }
public static Tuple<long, long>[] TupleLong(int n) { List<Tuple<long, long>> list = new List<Tuple<long, long>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<long, long>(ab[0], ab[1])); } return list.ToArray(); }
public static Tuple<string, string>[] TupleStr(int n) { List<Tuple<string, string>> list = new List<Tuple<string, string>>(); for (int i = 0; i < n; ++i) { var ab = Read.StrN(); list.Add(new Tuple<string, string>(ab[0], ab[1])); } return list.ToArray(); }
public static Tuple<double, double>[] TupleDouble(int n) { List<Tuple<double, double>> list = new List<Tuple<double, double>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<double, double>(ab[0], ab[1])); } return list.ToArray(); }
public static long[,] LongMatrix(int r, int c) { var mat = new long[r, c]; for (int i = 0; i < r; ++i) { var x = Read.LongN(); for (int j = 0; j < c; ++j) { mat[i, j] = x[j]; } } return mat; }
public static Dictionary<int, HashSet<int>> AdjacencyList(int N, int M, bool isDirectional = false)
{
Dictionary<int, HashSet<int>> dict = new Dictionary<int, HashSet<int>>();
for (int i = 0; i <= N; ++i) { dict.Add(i, new HashSet<int>()); }
        for (int i = 0; i < M; ++i) { var ab = Read.IntN(); if (!dict[ab[0]].Contains(ab[1])) { dict[ab[0]].Add(ab[1]); } if (!isDirectional && !dict[ab[1]].Contains(ab[0])) { dict[ab[1]].Add(ab[0]); } }
        return dict;
}
public static Dictionary<int, Dictionary<int, long>> AdjacencyListWithWeight(int N, int M)
{
Dictionary<int, Dictionary<int, long>> dict = new Dictionary<int, Dictionary<int, long>>(); for (int i = 0; i <= N; ++i) { dict.Add(i, new Dictionary<int, long>()); }
for (int i = 0; i < M; ++i) { var ab = Read.IntN(); dict[ab[0]].Add(ab[1], ab[2]); dict[ab[1]].Add(ab[0], ab[2]); }
return dict;
}
}
    }
}