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.Generic;
using System.IO;
using System.Linq;
using System.Numerics;

namespace CompetitionPrograming2
{
    public sealed class Program : BaseProgram
    {
        public static void Main(string[] _) { using (new SetConsole()) { Solve(); } }
        public static void Solve()
        {
            var abhm = GetArray<int>();
            var a = abhm[0];
            var b = abhm[1];
            var h = abhm[2];
            var m = abhm[3];

            var shortKakudo = m * 6;
            var longKakudo = h * 30 + 0.5 * m;
            var kakudo = longKakudo - shortKakudo;
            if (180 < kakudo)
            {
                kakudo = 360 - kakudo;
            }

            Write(Math.Sqrt(a * a + b * b - 2 * a * b * Math.Cos(ToRadian(kakudo))));
        }

        public static double ToRadian(double angle)
        {
            return (double)(angle * Math.PI / 180);
        }
    }
    public abstract class BaseProgram
    {
        protected readonly static long divisor = 1000000007;
        protected static Action<object> Write => Console.WriteLine;
        protected static string GetString()
        {
            var str = Console.ReadLine();
            if (str == null) { throw new NullReferenceException("標準入力がnullです Solveメソッド内の解答コードが間違っています"); }
            return str;
        }
        protected static T GetNumber<T>() where T : IComparable, IComparable<T>, IConvertible, IEquatable<T>, IFormattable
        {
            var str = GetString();
            var t = typeof(T);
            try
            {
                if (t == typeof(int))
                {
                    return (T)(object)str.ToInt();
                }
                else if (t == typeof(long))
                {
                    return (T)(object)str.ToLong();
                }
                else if (t == typeof(double))
                {
                    return (T)(object)str.ToDouble();
                }
                else if (t == typeof(decimal))
                {
                    return (T)(object)str.ToDecimal();
                }
                else if (t == typeof(BigInteger))
                {
                    return (T)(object)str.ToBigInteger();
                }
            }
            catch (OverflowException)
            {
                throw new OverflowException("より大きい数値型を指定してください");
            }
            throw new NotSupportedException();
        }
        protected static T[] GetArray<T>() where T : IComparable, IComparable<T>, IConvertible, IEquatable<T> => ToArray<T>(GetString());
        protected static List<T> GetList<T>() where T : IComparable, IComparable<T>, IConvertible, IEquatable<T> => ToList<T>(GetString());
        protected static void Swap<T>(ref T item1, ref T item2)
        {
            var tmp = item1;
            item1 = item2;
            item2 = tmp;
        }
        protected static IEnumerable<char> AtoZ()
        {
            for (char i = 'a'; i <= 'z'; i++)
            {
                yield return i;
            }
        }
        private static T[] ToArray<T>(string str) where T : IComparable, IComparable<T>, IConvertible, IEquatable<T>
        {
            return ConvertEnumerator<T>(str).ToArray();
        }
        private static List<T> ToList<T>(string str) where T : IComparable, IComparable<T>, IConvertible, IEquatable<T>
        {
            if (typeof(T) == typeof(string)) { return (List<T>)(object)str.Split().ToList(); }

            return ConvertEnumerator<T>(str).ToList();
        }
        private static IEnumerable<T> ConvertEnumerator<T>(string str) where T : IComparable, IComparable<T>, IConvertible, IEquatable<T>
        {
            var t = typeof(T);
            if (t == typeof(byte))
            {
                return str.Split().Select(byte.Parse).Cast<T>();
            }
            if (t == typeof(int))
            {
                return str.Split().Select(int.Parse).Cast<T>();
            }
            if (t == typeof(long))
            {
                return str.Split().Select(long.Parse).Cast<T>();
            }
            if (t == typeof(double))
            {
                return str.Split().Select(double.Parse).Cast<T>();
            }
            if (t == typeof(decimal))
            {
                return str.Split().Select(decimal.Parse).Cast<T>();
            }
            if (t == typeof(BigInteger))
            {
                return str.Split().Select(BigInteger.Parse).Cast<T>();
            }
            throw new NotSupportedException();
        }
        protected sealed class SetConsole : IDisposable
        {
            readonly StreamWriter sw = new StreamWriter(Console.OpenStandardOutput());
            public SetConsole()
            {
                sw.AutoFlush = false;
                Console.SetOut(sw);
            }
            public void Dispose()
            {
                Console.Out.Flush();
                sw.AutoFlush = true;
                Console.SetOut(sw);
            }
        }
    }
    public static class ExtentionsLibrary
    {
        public static long Choose(this int n, int a, long divisor = 1000000007)
        {
            long numerator = 1, denominator = 1;
            for (int i = 0; i < a; i++)
            {
                numerator *= n - i;
                numerator %= divisor;
                denominator *= i + 1;
                denominator %= divisor;
            }
            return numerator / denominator;
        }
        /// <summary>
        /// 階乗を求める
        /// </summary>
        /// <param name="num"></param>
        /// <returns></returns>
        public static long Factorial(this long num)
        {
            var result = 1L;
            for (int i = 1; i <= num; i++)
            {
                result *= i;
            }
            return result;
        }
        private static T[] NextPermutation<T>(this IEnumerable<T> collection, IComparer<T> cmp) where T : IComparable
        {
            var array = collection.ToArray();
            int? exchangingNumIndex = null;
            for (int i = 1; i < array.Length; i++)
            {
                if (cmp.Compare(array[i - 1], array[i]) >= 0) { continue; }

                exchangingNumIndex = i - 1;
            }

            if (exchangingNumIndex == null) { return null; }

            for (int j = array.Length - 1; j >= 0; j--)
            {
                if (cmp.Compare(array[(int)exchangingNumIndex], array[j]) >= 0) { continue; }

                var tmp = array[j];
                array[j] = array[(int)exchangingNumIndex];
                array[(int)exchangingNumIndex] = tmp;
                array = array.Take((int)exchangingNumIndex + 1).Concat(array.Skip((int)exchangingNumIndex + 1).Reverse()).ToArray();
                break;
            }
            return array;
        }
        public static string[] NextPermutation(this IEnumerable<string> collection)
        {
            return NextPermutation(collection, StringComparer.Ordinal);
        }
        public static T[] NextPermutation<T>(this IEnumerable<T> collection) where T : IComparable
        {
            return NextPermutation(collection, Comparer<T>.Default);
        }
        public static IEnumerable<T[]> Permutations<T>(this IEnumerable<T> collection) where T : IComparable
        {
            var next = collection.NextPermutation();

            while (next != null)
            {
                yield return next;

                next = next.NextPermutation();
            }
        }
        public static long Gcd(this long a, long b)
        {
            if (a < b) { return Gcd(b, a); }
            long tmp;
            do
            {
                tmp = a % b;
                a = b;
                b = tmp;
            } while (tmp != 0);
            return a;
        }
        /// <summary>
        /// 素因数分解を行う
        /// </summary>
        /// <param name="num"></param>
        /// <returns></returns>
        public static IEnumerable<Tuple<long, int>> Factorize(this long n)
        {
            yield return Tuple.Create(1L, 1);
            var rootN = Math.Sqrt(n);
            for (long i = 2; i <= rootN; i++)
            {
                if (n % i != 0) { continue; }

                var count = 1;
                n /= i;
                while (n % i == 0)
                {
                    n /= i;
                    count++;
                }
                yield return Tuple.Create(i, count);
            }
            if (n != 1) { yield return Tuple.Create(n, 1); }
        }
        public static int ToInt(this string str) => int.Parse(str);
        public static int ToInt(this char chr) => int.Parse(chr.ToString());
        public static long ToLong(this string str) => long.Parse(str);
        public static double ToDouble(this string str) => double.Parse(str);
        public static decimal ToDecimal(this string str) => decimal.Parse(str);
        public static BigInteger ToBigInteger(this string str) => BigInteger.Parse(str);
        public static DateTime ToDateTime(this string str) => DateTime.Parse(str);
        public static string StringJoin<T>(this IEnumerable<T> collection, string separator = "") => string.Join(separator, collection.Select(c => c.ToString()));
        public static string StringConcat(this IEnumerable<char> collection) => string.Concat(collection);
        public static int LowerBound<T>(this IReadOnlyList<T> a, T v) => LowerBound(a, v, Comparer<T>.Default);
        public static int LowerBound(this IReadOnlyList<string> str, string v) => LowerBound(str, v, StringComparer.Ordinal);
        public static int LowerBound<T>(this IReadOnlyList<T> a, T v, IComparer<T> cmp)
        {
            var l = 0;
            var r = a.Count - 1;
            while (l <= r)
            {
                var mid = l + (r - l) / 2;
                var result = cmp.Compare(a[mid], v);
                if (result == -1)
                {
                    l = mid + 1;
                }
                else
                {
                    r = mid - 1;
                }
            }
            return l;
        }
        public static int UpperBound(this IReadOnlyList<string> str, string v) => UpperBound(str, v, StringComparer.Ordinal);
        public static int UpperBound<T>(this IReadOnlyList<T> a, T v) => UpperBound(a, v, Comparer<T>.Default);
        public static int UpperBound<T>(this IReadOnlyList<T> a, T v, IComparer<T> cmp)
        {
            var l = 0;
            var r = a.Count - 1;
            while (l <= r)
            {
                var mid = l + (r - l) / 2;
                var res = cmp.Compare(a[mid], v);
                if (res <= 0) l = mid + 1;
                else r = mid - 1;
            }
            return l;
        }
        public static IOrderedEnumerable<TSource> OrderBy<TSource>(this IEnumerable<TSource> source, Func<TSource, string> keySelector)
        {
            return source.OrderBy(keySelector, StringComparer.Ordinal);
        }
        public static IOrderedEnumerable<TSource> OrderByDescending<TSource>(this IEnumerable<TSource> source, Func<TSource, string> keySelector)
        {
            return source.OrderByDescending(keySelector, StringComparer.Ordinal);
        }
    }

    public struct Mint
    {
        private static readonly long MOD = (long)1e9 + 7;

        /// <summary>
        /// 0以上MOD未満の整数
        /// </summary>
        public long Value;

        public Mint(long val)
        {
            Value = val % MOD;
            if (Value < 0) Value += MOD;
        }

        private static Mint Ctor(long val) => new Mint() { Value = val };
        public static Mint operator +(Mint a, Mint b)
        {
            long res = a.Value + b.Value;
            if (res > MOD) res -= MOD;
            return Ctor(res);
        }
        public static Mint operator -(Mint a, Mint b)
        {
            long res = a.Value - b.Value;
            if (res < 0) res += MOD;
            return Ctor(res);
        }
        public static Mint operator *(Mint a, Mint b)
        {
            long res = a.Value * b.Value;
            if (res > MOD) res %= MOD;
            return Ctor(res);
        }
        public static Mint operator /(Mint a, Mint b) => a * Inv(b);
        public static Mint Pow(Mint a, long n)
        {
            if (n == 0) return new Mint(1);
            Mint b = Pow(a, n >> 1);
            b *= b;
            if ((n & 1) == 1) b *= a;
            return b;
        }
        public static Mint Inv(Mint n)
        {
            long a = n.Value;
            long b = MOD;

            long x = 1;
            long u = 0;
            while (b != 0)
            {
                long k = a / b;
                long _x = u;
                u = x - k * u;
                x = _x;

                long _a = a;
                a = b;
                b = _a - (k * b);
            }

            return new Mint(x);
        }
        public override string ToString() => Value.ToString();
        public static implicit operator Mint(long a) => new Mint(a);
        public static explicit operator long(Mint a) => a.Value;
        public static Mint Choose(long n, long k)
        {
            Mint numerator = 1, denominator = 1;
            for (int i = 0; i < k; i++)
            {
                numerator *= n - i;
                denominator *= i + 1;
            }
            return numerator / denominator;
        }
    }
    public enum Priority : byte
    {
        Smaller = 0,
        Larger = 1
    }
}