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++14 (GCC 5.4.1) (judge verdict: Accepted)

#define _USE_MATH_DEFINES
#ifdef __GNUC__
#include <bits/stdc++.h>
#else
#define _CRT_SECURE_NO_WARNINGS
#include <__msvc_all_public_headers.hpp>
#undef min
#undef max
#endif
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define FOR(i, m, n) for (int i = (m); i < (n); ++i)
#define rrep(i, n) for (int i = (n) - 1; i >= 0; --i)
#define rfor(i, m, n) for (int i = (m); i >= (n); --i)
#define sz(x) ((int)(x).size())
#define all(x) (x).begin(),(x).end()
#define rall(x) (x).rbegin(),(x).rend()
#define range_it(a, l, r) (a).begin() + (l), (a).begin() + (r)

using namespace std;
using ll = long long;		using ld = long double;
using VB = vector<bool>;	using VVB = vector<VB>;
using VI = vector<int>;		using VVI = vector<VI>;
using VL = vector<ll>;		using VVL = vector<VL>;
using VS = vector<string>;	using VD = vector<ld>;
using PII = pair<int, int>;	using VP = vector<PII>;
using PLL = pair<ll, ll>;	using VPL = vector<PLL>;
template<class T>using PQ = priority_queue<T>;
template<class T>using PQS = priority_queue<T, vector<T>, greater<T>>;
constexpr int inf = (int)1e9;
constexpr ll inf_ll = (ll)1e18, MOD = 1000000007;
constexpr ld PI = M_PI, EPS = 1e-12;

// --- input --- //
#ifdef _WIN32
#define getchar_unlocked _getchar_nolock
#define putchar_unlocked _putchar_nolock
#define fwrite_unlocked _fwrite_nolock
#define fflush_unlocked _fflush_nolock
#endif
inline int gc() { return getchar_unlocked(); }
template<class T>inline void InputF(T& v) { cin >> v; }
inline void InputF(char& v) { while (isspace(v = gc())); }
inline void InputF(bool& v) { char c; InputF(c); v = c != '0'; }
inline void InputF(string& v) {
	char c; for (InputF(c); !isspace(c); c = gc())v += c;
}
inline void InputF(int& v) {
	bool neg = false; v = 0; char c; InputF(c);
	if (c == '-') { neg = true; c = gc(); }
	for (; isdigit(c); c = gc())v = v * 10 + (c - '0');
	if (neg)v = -v;
}
inline void InputF(long long& v) {
	bool neg = false; v = 0; char c; InputF(c);
	if (c == '-') { neg = true; c = gc(); }
	for (; isdigit(c); c = gc())v = v * 10 + (c - '0');
	if (neg)v = -v;
}
inline void InputF(double& v) {
	double dp = 1; bool neg = false, adp = false; v = 0; char c; InputF(c);
	if (c == '-') { neg = true; c = gc(); }
	for (; isdigit(c) || c == '.'; c = gc()) {
		if (c == '.')adp = true;
		else if (adp)v += (c - '0') * (dp *= 0.1);
		else v = v * 10 + (c - '0');
	}
	if (neg)v = -v;
}
template<class T, class U>inline void InputF(pair<T, U>& v) {
	InputF(v.first); InputF(v.second);
}
template<class T>inline void InputF(vector<T>& v) {
	for (auto& e : v)InputF(e);
}
template<class T>inline T InputF() { T v; InputF(v); return v; }
inline string GetLine() {
	string v; char c; for (InputF(c); c != '\n' && c != '\0'; c = gc())v += c; return v;
}
struct InputV {
	int n, m;
	InputV(int N) :n(N), m(0) {}
	InputV(pair<int, int> N) :n(N.first), m(N.second) {}
	template<class T>operator vector<T>() {
		vector<T> v(n); InputF(v); return v;
	}
	template<class T>operator vector<vector<T>>() {
		vector<vector<T>> v(n, vector<T>(m)); InputF(v); return v;
	}
};
struct Input {
	template<class T>operator T() { return InputF<T>(); }
	int operator--(int) { int v; InputF(v); v--; return v; }
	InputV operator[](int n) { return InputV(n); }
	InputV operator[](pair<int, int> n) { return InputV(n); }
	void operator()() {}
	template<class H, class...T>void operator()(H&& h, T&& ...t) {
		InputF(h); operator()(forward<T>(t)...);
	}
	template<class T>Input& operator,(T&& v) {
		InputF(v); return *this;
	}
}in;
#define input(T) InputF<T>()
#define ini input(int)
#define inl input(ll)
#define ins input(string)
#define inputs(T, ...) T __VA_ARGS__; in(__VA_ARGS__)
#define INT(...) inputs(int, __VA_ARGS__)
#define LL(...) inputs(ll, __VA_ARGS__)
#define STR(...) inputs(string, __VA_ARGS__)

// --- output --- //
struct BoolStr {
	const char* t, * f; BoolStr(const char* _t, const char* _f) :t(_t), f(_f) {}
}Yes("Yes", "No"), yes("yes", "no"), YES("YES", "NO"), Int("1", "0");
struct DivStr {
	const char* d, * l; DivStr(const char* _d, const char* _l) :d(_d), l(_l) {}
}spc(" ", "\n"), no_spc("", "\n"), end_line("\n", "\n"), comma(",", "\n"), no_endl(" ", "");
class Output {
	BoolStr B{ Yes }; DivStr D{ spc };
	void p(int v) {
		if (v < 0)putchar_unlocked('-'), v = -v;
		char b[10]; int n = 0;
		while (v)b[n++] = '0' + v % 10, v /= 10;
		if (!n)b[n++] = '0';
		while (n--)putchar_unlocked(b[n]);
	}
	void p(ll v) {
		if (v < 0)putchar_unlocked('-'), v = -v;
		char b[20]; int n = 0;
		while (v)b[n++] = '0' + v % 10, v /= 10;
		if (!n)b[n++] = '0';
		while (n--)putchar_unlocked(b[n]);
	}
	void p(bool v) { p(v ? B.t : B.f); }
	void p(char v) { putchar_unlocked(v); }
	void p(const char* v) { fwrite_unlocked(v, 1, strlen(v), stdout); }
	void p(double v) { printf("%.20f", v); }
	void p(ld v) { printf("%.20Lf", v); }
	template<class T> void p(const T& v) { cout << v; }
	template<class T, class U>void p(const pair<T, U>& v) { p(v.first); p(D.d); p(v.second); }
	template<class T>void p(const vector<T>& v) { rep(i, sz(v)) { if (i)p(D.d); p(v[i]); } }
	template<class T>void p(const vector<vector<T>>& v) { rep(i, sz(v)) { if (i)p(D.l); p(v[i]); } }
public:
	Output& operator()() { p(D.l); return *this; }
	template<class H>Output& operator()(H&& h) { p(h); p(D.l); return *this; }
	template<class H, class...T>Output& operator()(H&& h, T&& ...t) {
		p(h); p(D.d); return operator()(forward<T>(t)...);
	}
	template<class...T>void exit(T&& ...t) { operator()(forward<T>(t)...); std::exit(EXIT_SUCCESS); }
	Output& flush() { fflush_unlocked(stdout); return *this; }
	Output& set(const BoolStr& b) { B = b; return *this; }
	Output& set(const DivStr& d) { D = d; return *this; }
	Output& set(const char* t, const char* f) { B = BoolStr(t, f); return *this; }
}out;

// --- step --- //
template<class T>struct Step {
	class It {
		T a, b, c;
	public:
		constexpr It() : a(T()), b(T()), c(T()) {}
		constexpr It(T _b, T _c, T _s) : a(_b), b(_c), c(_s) {}
		constexpr It& operator++() { --b; a += c; return *this; }
		constexpr It operator++(int) { It tmp = *this; --b; a += c; return tmp; }
		constexpr const T& operator*()const { return a; }
		constexpr const T* operator->()const { return &a; }
		constexpr bool operator==(const It& i)const { return b == i.b; }
		constexpr bool operator!=(const It& i)const { return !(b == i.b); }
		constexpr T start()const { return a; }
		constexpr T count()const { return b; }
		constexpr T step()const { return c; }
	};
	constexpr Step(T b, T c, T s) : be(b, c, s) {}
	constexpr It begin()const { return be; }
	constexpr It end()const { return en; }
	constexpr T start()const { return be.start(); }
	constexpr T count()const { return be.count(); }
	constexpr T step()const { return be.step(); }
	constexpr T sum()const { return start() * count() + step() * (count() * (count() - 1) / 2); }
	operator vector<T>()const { return as_vector(); }
	vector<T> as_vector()const {
		vector<T> res; res.reserve(count()); each([&](T i) {res.push_back(i); }); return res;
	}
	template<class F>void each(const F& f)const { for (T i : *this)f(i); }
	template<class F>auto map(const F& f)const {
		vector<decay_t<result_of_t<F(T)>>> res; res.reserve(count());
		each([&](T i) {res.push_back(f(i)); }); return res;
	}
	template<class F>int count_if(const F& f)const {
		int res = 0; each([&](T i) {res += static_cast<bool>(f(i)); }); return res;
	}
	template<class F>vector<T> select(const F& f)const {
		vector<T> res; each([&](T i) {if (f(i))res.push_back(i); }); return res;
	}
	template<class F>auto max(const F& f)const {
		auto v = map(f); return *max_element(v.begin(), v.end());
	}
	template<class F>auto min(const F& f)const {
		auto v = map(f); return *min_element(v.begin(), v.end());
	}
	template<class F, class U = decay_t<result_of_t<F(T)>>>auto sum(const F& f)const {
		U res = 0; each([&](T i) {res += static_cast<U>(f(i)); }); return res;
	}
	using value_type = T;
	using iterator = It;
private:
	It be, en;
};
template<class T>inline constexpr auto step(T a) { return Step<T>(0, a, 1); }
template<class T>inline constexpr auto step(T a, T b) { return Step<T>(a, b - a, 1); }
template<class T>inline constexpr auto step(T a, T b, T c) { return Step<T>(a, a < b ? (b - a - 1) / c + 1 : 0, c); }

// --- functions --- //
inline namespace {
	template<class T>inline void Sort(T& a) { sort(all(a)); }
	template<class T>inline void RSort(T& a) { sort(rall(a)); }
	template<class T>inline T Sorted(T a) { Sort(a); return a; }
	template<class T>inline T RSorted(T a) { RSort(a); return a; }
	template<class T, class F>inline void Sort(T& a, const F& f) {
		sort(all(a), [&](const auto& x, const auto& y) {return f(x) < f(y); });
	}
	template<class T, class F>inline void RSort(T& a, const F& f) {
		sort(rall(a), [&](const auto& x, const auto& y) {return f(x) < f(y); });
	}
	template<class T>inline void Reverse(T& a) { reverse(all(a)); }
	template<class T>inline void Unique(T& a) { a.erase(unique(all(a)), a.end()); }
	template<class T>inline void Rotate(T& a, int left) { rotate(a.begin(), a.begin() + left, a.end()); }
	template<class T>inline T Reversed(T a) { Reverse(a); return a; }
	template<class T>inline T Uniqued(T a) { Unique(a); return a; }
	template<class T>inline T Rotated(T a, int left) { Rotate(a, left); return a; }
	template<class T>inline auto Max(const T& a) { return *max_element(all(a)); }
	template<class T>inline auto Min(const T& a) { return *min_element(all(a)); }
	template<class T>inline int MaxPos(const T& a) { return max_element(all(a)) - a.begin(); }
	template<class T>inline int MinPos(const T& a) { return min_element(all(a)) - a.begin(); }
	template<class T, class F>inline auto Max(const T& a, const F& f) {
		return *max_element(all(a), [&](const auto& x, const auto& y) {return f(x) < f(y); });
	}
	template<class T, class F>inline auto Min(const T& a, const F& f) {
		return *min_element(all(a), [&](const auto& x, const auto& y) {return f(x) < f(y); });
	}
	template<class T, class U>inline int Count(const T& a, const U& v) { return count(all(a), v); }
	template<class T, class F>inline int CountIf(const T& a, const F& f) { return count_if(all(a), f); }
	template<class T, class U>inline int Find(const T& a, const U& v) { return find(all(a), v) - a.begin(); }
	template<class T, class F>inline int FindIf(const T& a, const F& f) { return find_if(all(a), f) - a.begin(); }
	template<class T, class U = typename T::value_type>inline U Sum(const T& a) { return accumulate(all(a), U()); }
	template<class T, class F>inline auto Sum(const T& v, const F& f) {
		return accumulate(next(v.begin()), v.end(), f(v.front()), [&](auto a, auto b) {return a + f(b); });
	}
	template<class T, class U>inline int Lower(const T& a, const U& v) { return lower_bound(all(a), v) - a.begin(); }
	template<class T, class U>inline int Upper(const T& a, const U& v) { return upper_bound(all(a), v) - a.begin(); }
	template<class T, class F>inline void RemoveIf(T& a, const F& f) { a.erase(remove_if(all(a), f), a.end()); }
	template<class F>inline auto Vector(size_t size, const F& f) {
		vector<decay_t<result_of_t<F(size_t)>>> res(size); for (size_t i = 0; i < size; ++i)res[i] = f(i); return res;
	}
	template<class T>inline auto Grid(size_t h, size_t w, const T& v = T()) { return vector<vector<T>>(h, vector<T>(w, v)); }
	template<class T>inline auto Slice(const T& v, size_t i, size_t len) {
		return i < v.size() ? T(v.begin() + i, v.begin() + min(i + len, v.size())) : T();
	}
	template<class T, class F>inline auto Each(const T& v, const F& f) { for (auto& i : v)f(i); }
	template<class T, class F>inline auto Select(const T& v, const F& f) {
		T res; for (const auto& e : v)if (f(e))res.push_back(e); return res;
	}
	template<class T, class F>inline auto Map(const T& v, const F& f) {
		vector<decay_t<result_of_t<F(typename T::value_type)>>> res(v.size());
		size_t i = 0; for (const auto& e : v)res[i++] = f(e); return res;
	}
	template<class T, class F>inline auto MapIndex(const T& v, const F& f) {
		vector<decay_t<result_of_t<F(size_t, typename T::value_type)>>> res(v.size());
		size_t i = 0; for (auto it = v.begin(); it != v.end(); ++it, ++i)res[i] = f(i, *it); return res;
	}
	template<class T, class F>inline auto TrueIndex(const T& v, const F& f) {
		vector<size_t> res; for (size_t i = 0; i < v.size(); ++i)if (f(v[i]))res.push_back(i); return res;
	}
	inline string operator*(string s, size_t n) { string ret; for (size_t i = 0; i < n; ++i)ret += s; return ret; }
	template<class T>inline T Ceil(T n, T m) { return (n + m - 1) / m; }
	template<class T>inline T Ceil2(T n, T m) { return Ceil(n, m) * m; }
	template<class T>inline T Tri(T n) { return (n & 1) ? (n + 1) / 2 * n : n / 2 * (n + 1); }
	template<class T>inline T nC2(T n) { return (n & 1) ? (n - 1) / 2 * n : n / 2 * (n - 1); }
	template<class T>inline T Mid(const T& l, const T& r) { return l + (r - l) / 2; }
	template<class T>inline int pop_count(T n) { return bitset<64>(n).count(); }
	template<class T>inline bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } return false; }
	template<class T>inline bool chmin(T& a, const T& b) { if (a > b) { a = b; return true; } return false; }
	template<class T>inline bool inRange(const T& v, const T& min, const T& max) { return min <= v && v < max; }
	template<class T = ll>inline T BIT(int b) { return T(1) << b; }
	template<class T>inline T Gcd(T n, T m) { return m ? Gcd(m, n % m) : n; }
	template<class T>inline T Lcm(T n, T m) { return n / Gcd(n, m) * m; }
	template<class T, class U = typename T::value_type>inline U Gcdv(const T& v) {
		return accumulate(next(v.begin()), v.end(), U(*v.begin()), Gcd<U>);
	}
	template<class T, class U = typename T::value_type>inline U Lcmv(const T& v) {
		return accumulate(next(v.begin()), v.end(), U(*v.begin()), Lcm<U>);
	}
	template<class T>inline T Pow(T a, T n) { T r = 1; while (n > 0) { if (n & 1)r *= a; a *= a; n /= 2; } return r; }
	template<class T>inline T Powmod(T a, T n, T m = MOD) {
		T r = 1; while (n > 0) { if (n & 1)r = r * a % m, n--; else a = a * a % m, n /= 2; }return r;
	}
}

// --- dump --- //
#if __has_include("dump.hpp")
#include "dump.hpp"
#else
#define dump(...) ((void)0)
#endif

// ---------------------------------------------------------------- //

struct D {
	ll w, s;
	D(ll _w, ll _s) :w(_w), s(_s) {}
};
bool operator<(const D& d1, const D& d2) {
	return 100 * d1.s * (d2.s + d2.w) < 100 * d2.s * (d1.s + d1.w);
}

int main() {
	LL(a, b, c, d, e, f);

	D ans(a * 100, 0);
	rep(A, inf) {
		if (100 * a * A > f)break;
		rep(B, inf) {
			ll water = 100 * a * A + 100 * b * B;
			if (water > f)break;
			ll S = min(f - water, water / 100 * e);

			ll ma = 0;
			rep(C, inf) {
				if (c * C > S)break;
				ll D = (S - c * C) / d;
				chmax(ma, c * C + d * D);
			}
			chmax(ans, D(water, ma));
		}
	}
	out(ans.s + ans.w, ans.s);
}