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.Linq;
using static System.Math;
using static ABC168.abc168_c.Cin;
using static ABC168.abc168_c.Util;
using Pair = ABC168.abc168_c.VTuple<long, long>;

/// <summary>
/// ABC168
/// C - : (Colon)
/// https://atcoder.jp/contests/ABC168/tasks/abc168_c
/// </summary>
namespace ABC168.abc168_c
{
    public class Program
    {
        public static void Main(string[] args)
        {
            int A = ri;
            int B = ri;
            int H = ri;
            int M = ri;

            double x1, y1;
            {
                int angle = 30 * H;
                if (angle <= 90)
                {
                    double k = (90 - angle) * (Math.PI / 180);
                    x1 = Math.Cos(k) * A;
                    y1 = Math.Sin(k) * A;
                }
                else if (angle <= 180)
                {
                    double k = (angle - 90) * (Math.PI / 180);
                    x1 = Math.Cos(k) * A;
                    y1 = -Math.Sin(k) * A;
                }
                else if (angle <= 270)
                {
                    double k = (270 - angle) * (Math.PI / 180);
                    x1 = -Math.Cos(k) * A;
                    y1 = -Math.Sin(k) * A;
                }
                else
                {
                    double k = (angle - 270) * (Math.PI / 180);
                    x1 = -Math.Cos(k) * A;
                    y1 = Math.Sin(k) * A;
                }
            }

            double x2, y2;
            {
                int angle = 6 * M;
                if (angle <= 90)
                {
                    double k = (90 - angle) * (Math.PI / 180);
                    x2 = Math.Cos(k) * B;
                    y2 = Math.Sin(k) * B;
                }
                else if (angle <= 180)
                {
                    double k = (angle - 90) * (Math.PI / 180);
                    x2 = Math.Cos(k) * B;
                    y2 = -Math.Sin(k) * B;
                }
                else if (angle <= 270)
                {
                    double k = (270 - angle) * (Math.PI / 180);
                    x2 = -Math.Cos(k) * B;
                    y2 = -Math.Sin(k) * B;
                }
                else
                {
                    double k = (angle - 270) * (Math.PI / 180);
                    x2 = -Math.Cos(k) * B;
                    y2 = Math.Sin(k) * B;
                }
            }

            double ans = Math.Sqrt(Math.Pow(x1 - x2, 2) + Math.Pow(y1 - y2, 2));

            Console.WriteLine(ans);
        }
    }

    /// <summary>
    /// 競プロライブラリ
    /// https://github.com/ha2ne2/ABC/tree/master/Lib
    /// </summary>
    public struct Mint:System.IComparable<Mint>,System.IEquatable<Mint>{public static readonly long MOD=(long)1e9+7;public long Value;public Mint(long val){Value=val%MOD;if(Value<0)Value+=MOD;}private static Mint Ctor(long val){return 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){return a*Inv(b);}public override bool Equals(object obj){return obj is Mint&&Value==((Mint)obj).Value;}public override int GetHashCode(){return Value.GetHashCode();}public override string ToString(){return Value.ToString();}public static implicit operator Mint(long a){return new Mint(a);}public static explicit operator long(Mint a){return a.Value;}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 bool Equals(Mint other){return Value==other.Value;}public int CompareTo(Mint other){return Comparer<long>.Default.Compare(Value,other.Value);}}public class HashMap<K,V>:System.Collections.Generic.Dictionary<K,V>{private V DefaultValue;private static Func<V>CreateInstance=System.Linq.Expressions.Expression.Lambda<Func<V>>(System.Linq.Expressions.Expression.New(typeof(V))).Compile();public HashMap(){}public HashMap(V defaultValue){DefaultValue=defaultValue;}new public V this[K i]{get{V v;if(TryGetValue(i,out v)){return v;}else{return base[i]=DefaultValue!=null?DefaultValue:CreateInstance();}}set{base[i]=value;}}}public struct VTuple<T1,T2>:System.IComparable<VTuple<T1,T2>>,System.IEquatable<VTuple<T1,T2>>{public T1 Item1;public T2 Item2;public T1 First{get{return Item1;}}public T2 Second{get{return Item2;}}public VTuple(T1 item1,T2 item2){Item1=item1;Item2=item2;}public override bool Equals(object obj){return obj is VTuple<T1,T2>&&Equals((VTuple<T1,T2>)obj);}public override int GetHashCode(){int h1=Item1!=null?Item1.GetHashCode():0;int h2=Item2!=null?Item2.GetHashCode():0;return HashHelpers.CombineHashCodes(h1,h2);}public override string ToString(){return"("+Item1?.ToString()+", "+Item2?.ToString()+")";}public bool Equals(VTuple<T1,T2>other){return EqualityComparer<T1>.Default.Equals(Item1,other.Item1)&&EqualityComparer<T2>.Default.Equals(Item2,other.Item2);}public int CompareTo(VTuple<T1,T2>other){int c=Comparer<T1>.Default.Compare(Item1,other.Item1);if(c!=0)return c;return Comparer<T2>.Default.Compare(Item2,other.Item2);}}public struct VTuple3<T1,T2,T3>:System.IComparable<VTuple3<T1,T2,T3>>,System.IEquatable<VTuple3<T1,T2,T3>>{public T1 Item1;public T2 Item2;public T3 Item3;public VTuple3(T1 item1,T2 item2,T3 item3){Item1=item1;Item2=item2;Item3=item3;}public override bool Equals(object obj){return obj is VTuple3<T1,T2,T3>&&Equals((VTuple3<T1,T2,T3>)obj);}public override int GetHashCode(){int h1=Item1!=null?Item1.GetHashCode():0;int h2=Item2!=null?Item2.GetHashCode():0;int h3=Item3!=null?Item3.GetHashCode():0;return HashHelpers.CombineHashCodes(h1,h2,h3);}public override string ToString(){return"("+Item1?.ToString()+", "+Item2?.ToString()+", "+Item3?.ToString()+")";}public bool Equals(VTuple3<T1,T2,T3>other){return EqualityComparer<T1>.Default.Equals(Item1,other.Item1)&&EqualityComparer<T2>.Default.Equals(Item2,other.Item2)&&EqualityComparer<T3>.Default.Equals(Item3,other.Item3);}public int CompareTo(VTuple3<T1,T2,T3>other){int c=Comparer<T1>.Default.Compare(Item1,other.Item1);if(c!=0)return c;c=Comparer<T2>.Default.Compare(Item2,other.Item2);if(c!=0)return c;return Comparer<T3>.Default.Compare(Item3,other.Item3);}}public struct VTuple4<T1,T2,T3,T4>:System.IComparable<VTuple4<T1,T2,T3,T4>>,System.IEquatable<VTuple4<T1,T2,T3,T4>>{public T1 Item1;public T2 Item2;public T3 Item3;public T4 Item4;public VTuple4(T1 item1,T2 item2,T3 item3,T4 item4){Item1=item1;Item2=item2;Item3=item3;Item4=item4;}public override bool Equals(object obj){return obj is VTuple4<T1,T2,T3,T4>&&Equals((VTuple4<T1,T2,T3,T4>)obj);}public override int GetHashCode(){int h1=Item1!=null?Item1.GetHashCode():0;int h2=Item2!=null?Item2.GetHashCode():0;int h3=Item3!=null?Item3.GetHashCode():0;int h4=Item3!=null?Item4.GetHashCode():0;return HashHelpers.CombineHashCodes(h1,h2,h3,h4);}public override string ToString(){return"("+Item1?.ToString()+", "+Item2?.ToString()+", "+Item3?.ToString()+", "+Item4?.ToString()+")";}public bool Equals(VTuple4<T1,T2,T3,T4>other){return EqualityComparer<T1>.Default.Equals(Item1,other.Item1)&&EqualityComparer<T2>.Default.Equals(Item2,other.Item2)&&EqualityComparer<T3>.Default.Equals(Item3,other.Item3)&&EqualityComparer<T4>.Default.Equals(Item4,other.Item4);}public int CompareTo(VTuple4<T1,T2,T3,T4>other){int c=Comparer<T1>.Default.Compare(Item1,other.Item1);if(c!=0)return c;c=Comparer<T2>.Default.Compare(Item2,other.Item2);if(c!=0)return c;c=Comparer<T3>.Default.Compare(Item3,other.Item3);if(c!=0)return c;return Comparer<T4>.Default.Compare(Item4,other.Item4);}}public static class HashHelpers{public static readonly int RandomSeed=new System.Random().Next(int.MinValue,int.MaxValue);public static int Combine(int h1,int h2){uint rol5=((uint)h1<<5)|((uint)h1>>27);return((int)rol5+h1)^h2;}public static int CombineHashCodes(int h1,int h2){return Combine(Combine(RandomSeed,h1),h2);}public static int CombineHashCodes(int h1,int h2,int h3){return Combine(CombineHashCodes(h1,h2),h3);}public static int CombineHashCodes(int h1,int h2,int h3,int h4){return Combine(CombineHashCodes(h1,h2,h3),h4);}}public static class Cin{public static int ri{get{return ReadInt();}}public static int[]ria{get{return ReadIntArray();}}public static long rl{get{return ReadLong();}}public static long[]rla{get{return ReadLongArray();}}public static double rd{get{return ReadDouble();}}public static double[]rda{get{return ReadDoubleArray();}}public static string rs{get{return ReadString();}}public static string[]rsa{get{return ReadStringArray();}}public static int ReadInt(){return int.Parse(Next());}public static long ReadLong(){return long.Parse(Next());}public static double ReadDouble(){return double.Parse(Next());}public static string ReadString(){return Next();}public static int[]ReadIntArray(){Tokens=null;return Array.ConvertAll(Console.ReadLine().Split(' '),int.Parse);}public static long[]ReadLongArray(){Tokens=null;return Array.ConvertAll(Console.ReadLine().Split(' '),long.Parse);}public static double[]ReadDoubleArray(){Tokens=null;return Array.ConvertAll(Console.ReadLine().Split(' '),double.Parse);}public static string[]ReadStringArray(){Tokens=null;return Console.ReadLine().Split(' ');}public static void ReadCol(out long[]a,long N){a=new long[N];for(int i=0;i<N;i++){a[i]=ReadLong();}}public static void ReadCols(out long[]a,out long[]b,long N){a=new long[N];b=new long[N];for(int i=0;i<N;i++){a[i]=ReadLong();b[i]=ReadLong();}}public static void ReadCols(out long[]a,out long[]b,out long[]c,long N){a=new long[N];b=new long[N];c=new long[N];for(int i=0;i<N;i++){a[i]=ReadLong();b[i]=ReadLong();c[i]=ReadLong();}}public static int[,]ReadIntTable(int h,int w){Tokens=null;int[,]ret=new int[h,w];for(int i=0;i<h;i++){for(int j=0;j<w;j++){ret[i,j]=ReadInt();}}return ret;}public static long[,]ReadLongTable(long h,long w){Tokens=null;long[,]ret=new long[h,w];for(int i=0;i<h;i++){for(int j=0;j<w;j++){ret[i,j]=ReadLong();}}return ret;}public static char[,]ReadCharTable(int h,int w){Tokens=null;char[,]res=new char[h,w];for(int i=0;i<h;i++){string s=ReadString();for(int j=0;j<w;j++){res[i,j]=s[j];}}return res;}private static string[]Tokens;private static int Pointer;private static string Next(){if(Tokens==null||Tokens.Length<=Pointer){Tokens=Console.ReadLine().Split(' ');Pointer=0;}return Tokens[Pointer++];}}public static class Util{public static readonly long INF=(long)1e17;public readonly static long MOD=(long)1e9+7;public readonly static int[]DXY4={0,1,0,-1,0};public readonly static int[]DXY8={1,1,0,1,-1,0,-1,-1,1};public static void DontAutoFlush(){if(Console.IsOutputRedirected)return;var sw=new System.IO.StreamWriter(Console.OpenStandardOutput()){AutoFlush=false};Console.SetOut(sw);}public static void Flush(){Console.Out.Flush();}public static T[]Sort<T>(T[]array){Array.Sort<T>(array);return array;}public static T[]SortDecend<T>(T[]array){Array.Sort<T>(array);Array.Reverse(array);return array;}public static void Swap<T>(ref T a,ref T b){T _a=a;a=b;b=_a;}public static long GCD(long a,long b){while(b!=0){long _a=a;a=b;b=_a%b;}return a;}public static long LCM(long a,long b){if(a==0||b==0)return 0;return a*b/GCD(a,b);}public static void ChMax(ref long a,long b){if(a<b)a=b;}public static void ChMin(ref long a,long b){if(a>b)a=b;}public static void ChMax(ref int a,int b){if(a<b)a=b;}public static void ChMin(ref int a,int b){if(a>b)a=b;}public static void FillArray<T>(T[]array,T value){int max=array.Length;for(int i=0;i<max;i++){array[i]=value;}}public static void FillArray<T>(T[,]array,T value){int max0=array.GetLength(0);int max1=array.GetLength(1);for(int i=0;i<max0;i++){for(int j=0;j<max1;j++){array[i,j]=value;}}}public static void FillArray<T>(T[,,]array,T value){int max0=array.GetLength(0);int max1=array.GetLength(1);int max2=array.GetLength(2);for(int i=0;i<max0;i++){for(int j=0;j<max1;j++){for(int k=0;k<max2;k++){array[i,j,k]=value;}}}}public static long[]Accumulate(long[]array){long[]acc=new long[array.Length+1];for(int i=0;i<array.Length;i++){acc[i+1]=acc[i]+array[i];}return acc;}public static double[]Accumulate(double[]array){double[]acc=new double[array.Length+1];for(int i=0;i<array.Length;i++){acc[i+1]=acc[i]+array[i];}return acc;}}
}