Problem:
Score : 300 points

Problem Statement

Snuke is making sugar water in a beaker.
Initially, the beaker is empty. Snuke can perform the following four types of operations any number of times. He may choose not to perform some types of operations.

Operation 1: Pour 100A grams of water into the beaker.

Operation 2: Pour 100B grams of water into the beaker.

Operation 3: Put C grams of sugar into the beaker.

Operation 4: Put D grams of sugar into the beaker.

In our experimental environment, E grams of sugar can dissolve into 100 grams of water.

Snuke will make sugar water with the highest possible density.

The beaker can contain at most F grams of substances (water and sugar combined), and there must not be any undissolved sugar in the beaker.
Find the mass of the sugar water Snuke will make, and the mass of sugar dissolved in it.
If there is more than one candidate, any of them will be accepted.

We remind you that the sugar water that contains a grams of water and b grams of sugar is \frac{100b}{a + b} percent.
Also, in this problem, pure water that does not contain any sugar is regarded as 0 percent density sugar water.

Constraints

1 \leq A < B \leq 30

1 \leq C < D \leq 30

1 \leq E \leq 100

100A \leq F \leq 3 000

A, B, C, D, E and F are all integers.

Inputs

Input is given from Standard Input in the following format:

A B C D E F

Outputs

Print two integers separated by a space.
The first integer should be the mass of the desired sugar water, and the second should be the mass of the sugar dissolved in it.

Sample Input 1

1 2 10 20 15 200

Sample Output 1

110 10

In this environment, 15 grams of sugar can dissolve into 100 grams of water, and the beaker can contain at most 200 grams of substances.

We can make 110 grams of sugar water by performing Operation 1 once and Operation 3 once.
It is not possible to make sugar water with higher density.
For example, the following sequences of operations are infeasible:

If we perform Operation 1 once and Operation 4 once, there will be undissolved sugar in the beaker.

If we perform Operation 2 once and Operation 3 three times, the mass of substances in the beaker will exceed 200 grams.

Sample Input 2

1 2 1 2 100 1000

Sample Output 2

200 100

There are other acceptable outputs, such as:

400 200

However, the output below is not acceptable:

300 150

This is because, in order to make 300 grams of sugar water containing 150 grams of sugar, we need to pour exactly 150 grams of water into the beaker, which is impossible.

Sample Input 3

17 19 22 26 55 2802

Sample Output 3

2634 934

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Math;
using static _20200412.arc083_a.Cin;
using static _20200412.arc083_a.Util;
using Pair = _20200412.arc083_a.VTuple<long, long>;

/// <summary>
/// abc074
/// C - Sugar Water
/// https://atcoder.jp/contests/abc074/tasks/arc083_a
/// </summary>
namespace _20200412.arc083_a
{
    public class Program
    {
        public static void Main(string[] args)
        {
            int[] W = new int[2] { ri, ri };
            int[] S = new int[2] { ri, ri };
            int E = ri;
            int F = ri;

            bool[] ok = new bool[F + 1];
            int[] dp = new int[F + 1];
            ok[0] = true;
            for (int i = 0; i <= F; i++)
            {
                if (!ok[i])
                    continue;

                for (int j = 0; j < 2; j++)
                {
                    if (j + 100 * W[j] <= F)
                    {
                        dp[j + 100 * W[j]] = Max(dp[j], dp[j + 100 * W[j]]);
                        ok[j + 100 * W[j]] = true;
                    }
                }

                for (int j = 0; j < 2; j++)
                {
                    if (i + S[j] <= F &&                                // コップから溢れず
                        dp[i] + S[j] <= (i + S[j]) * E / (100d + E) && // 砂糖が残らず
                        dp[i + S[j]] < dp[i] + S[j])                  // 今よりいい場合
                    {
                        dp[i + S[j]] = dp[i] + S[j];
                        ok[i + S[j]] = true;
                    }
                }
            }

            double max = 0;
            int idx = 1;
            for (int i = 1; i <= F; i++)
            {
                double nm = dp[i] * 100d / i;
                if (max < nm)
                {
                    max = nm;
                    idx = i;
                }
            }

            Console.WriteLine(idx + " " + dp[idx]);
        }        
    }

    /// <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;}}
}