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: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Text;

namespace ARC083A
{
    class Program
    {
        public static void Solve(Input input)
        {
            var a = input.NextInt();
            var b = input.NextInt();
            var c = input.NextInt();
            var d = input.NextInt();
            var e = input.NextInt();
            var f = input.NextInt();

            var water = new List<int>();
            for (int i = 0; i < 30; i++)
            {
                for (int j = 0; j < 30; j++)
                {
                    var w = 100 * (a * i + b * j);
                    if (w <= f) water.Add(w);
                }
            }

            var sugar = new List<int>();
            for (int i = 0; i < f / c + 1; i++)
            {
                for (int j = 0; j < f / d + 1; j++)
                {
                    var s = c * i + d * j;
                    if (s <= f) sugar.Add(s);
                }
            }

            var max = new Tuple<int, int>(100 * a, 0);
            var density = 0.0;
            foreach (var w in water)
            {
                foreach (var s in sugar)
                {
                    if (w + s > f) continue;
                    if (w / 100 * e < s) continue;

                    var den = (double)s / (w + s);
                    if (den > density)
                    {
                        density = den;
                        max = new Tuple<int, int>(w, s);
                    }
                }
            }

            Console.WriteLine($"{max.Item1 + max.Item2} {max.Item2}");
        }

        #region Main
        public static void Main(string[] args)
        {
            // 出力が少ないときはこれをセットする方が時間かかるけれど
            // そのときにTLEするのはアルゴリズムが悪いせいだし、まあ良しとする
            var needsFlushOutput = true;
            if (needsFlushOutput)
            {
                // 細かく出力しないようにする
                var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
                Console.SetOut(sw);
            }

            // 通常は引数無しで、ファイルから読み出したい場合はpath指定する
            var input = new Input();
            // 仮想的に標準入力をセットする
            input.SetText("");

            Solve(input);

            Console.Out.Flush();
        }
        #endregion

        #region Competitive Template
#pragma warning disable CS0414
        static readonly int MOD = (int)1e9 + 7;
        static readonly int[] dx = { 1, 0, -1, 0 };
        static readonly int[] dy = { 0, 1, 0, -1 };
        /// <summary> 左上が原点 </summary>
        static readonly char[] dir = { 'R', 'U', 'L', 'D' };
#pragma warning restore CS0414

        public class Input
        {
            // 変な改行コードがたまに混じっているので、一応セパレート指定する
            // スペース単独指定の方がもちろん早い
            static readonly char[] separator = { ' ', '\r', '\n' };
            readonly StreamReader sr;
            readonly Queue<string> queue;

            /// <summary>
            /// 特定のファイルから読み出したい場合はpath指定する
            /// </summary>
            public Input(string path = "")
            {
                queue = new Queue<string>();

                if (string.IsNullOrEmpty(path)) { sr = new StreamReader(Console.OpenStandardInput()); }
                else { sr = new StreamReader(path); }
            }

            /// <summary>
            /// 入力予約
            /// </summary>
            public void SetText(IEnumerable<string> items)
            {
                foreach (var item in items)
                    SetText(item);
            }

            /// <summary>
            /// 入力予約
            /// </summary>
            public bool SetText(string s)
            {
                if (string.IsNullOrEmpty(s)) return false;

                foreach (var elem in s.Trim().Split(separator, StringSplitOptions.RemoveEmptyEntries))
                    queue.Enqueue(elem);

                return true;
            }

            /// <summary>
            /// 要素が存在するか
            /// </summary>
            public bool Any() => queue.Any() || Read();

            /// <summary>
            /// 内部queueに入力からの値をsplitして格納する
            /// </summary>
            bool Read()
            {
                if (!SetText(sr.ReadLine())) return false;

                if (!queue.Any()) return Read();

                return queue.Any();
            }

            /// <summary>
            /// 次のstringを一つ読み込む
            /// </summary>
            public string Next()
            {
                if (!queue.Any() && !Read()) return "";

                return queue.Dequeue();
            }

            /// <summary>
            /// 指定個数queueにたまるまでenqueueし続ける
            /// </summary>
            bool Accumulate(int n)
            {
                while (queue.Count() < n)
                    if (!Read()) return false;

                return true;
            }

            public int NextInt() => int.Parse(Next());
            public long NextLong() => long.Parse(Next());
            public double NextDouble() => double.Parse(Next());

            /// <summary>
            /// n個の要素をparseして、それぞれにoffsetをaddした配列を返す
            /// </summary>
            T[] NextT<T>(int n, T offset, Func<string, T> parse, Func<T, T, T> add)
            {
                if (!Accumulate(n)) return null;

                var a = new T[n];

                for (int i = 0; i < n; i++)
                    a[i] = add(parse(queue.Dequeue()), offset);

                return a;
            }

            public string[] Next(int n) => NextT(n, "", x => x, (x, y) => x);
            public int[] NextInt(int n, int offset = 0) => NextT(n, offset, int.Parse, (x, y) => x + y);
            public long[] NextLong(int n, long offset = 0) => NextT(n, offset, long.Parse, (x, y) => x + y);
            public double[] NextDouble(int n, double offset = 0.0) => NextT(n, offset, double.Parse, (x, y) => x + y);
        }

        static class Utils
        {
            public static T Max<T>(params T[] objs) => objs.Max();
            public static T Min<T>(params T[] objs) => objs.Min();

            /// <summary>
            /// vでfillされたT[d1][d2]配列を作成する
            /// </summary>
            public static T[][] Create2DArray<T>(int d1, int d2, T v)
            {
                return
                    Enumerable.Repeat(0, d1).Select(_ =>
                    Enumerable.Repeat(v, d2).ToArray()).ToArray();
            }

            /// <summary>
            /// vでfillされたT[d1][d2][d3]配列を作成する
            /// </summary>
            public static T[][][] Create3DArray<T>(int d1, int d2, int d3, T v)
            {
                return
                    Enumerable.Repeat(0, d1).Select(_ =>
                    Enumerable.Repeat(0, d2).Select(__ =>
                    Enumerable.Repeat(v, d3).ToArray()).ToArray()).ToArray();
            }
        }
        #endregion
    }
}