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++ (GCC 9.2.1) (judge verdict: Accepted)


/*
	@・ω・@
*/

// Memo:https://scrapbox.io/hitsujirere-memo/

/*****/

/**/
#pragma GCC target("avx")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
/**/

#include <bits/stdc++.h>

//#define int long long

using namespace std;
using ll = long long;
using ld = long double;
using pint = pair<int, int>;
using pll = pair<long long, long long>;
template <class T>
using vec = vector<T>;
template <class T>
using grapth = vec<vec<T>>;

#define rep(i, n) for (ll i = 0, i##_len = (n); i < i##_len; ++i)
#define rep1(i, n) for (ll i = 1, i##_len = (n); i <= i##_len; ++i)
#define rrep(i, n) for (ll i = (n)-1; i >= 0; --i)
#define rrep1(i, n) for (ll i = (n); i > 0; --i)
#define step(i, a, n) for (ll i = (a), i##_len = (a) + (n); i < i##_len; ++i)
#define rstep(i, a, n) for (ll i = (a) + (n)-1, i##_len = (a); i >= i##_len; --i)
#define range(i, a, b) for (ll i = (a), i##_len = (b); i < i##_len; ++i)
#define rrange(i, a, b) for (ll i = (b)-1, i##_len = (a); i >= i##_len; --i)

constexpr int INF = numeric_limits<int>::max();
constexpr ll INFL = numeric_limits<ll>::max();

std::string strMulti(const char c, const int n)
{
	std::string out = "";
	for (int i = 0; i < n; i++)
	{
		out += c;
	}
	return out;
}
std::string strMulti(const std::string t, const int n)
{
	std::string out = "";
	for (int i = 0; i < n; i++)
	{
		out += t;
	}
	return out;
}
std::string tab(const int n)
{
	return strMulti('\t', n);
}
std::string join(const vector<string> &v, const char *delim = 0)
{
	std::string s;
	if (!v.empty())
	{
		s += v[0];
		for (decltype(v.size()) i = 1, c = v.size(); i < c; ++i)
		{
			if (delim)
				s += delim;
			s += v[i];
		}
	}
	return s;
}

string to_string(string &s) { return '"' + s + '"'; }
string to_string(char &c) { return string({'\'', c, '\''}); }
template <class T1, class T2>
string to_string(pair<T1, T2> p)
{
	return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <class Tuple, size_t... I>
string _to_string_tuple(Tuple &&t, std::index_sequence<I...>)
{
	vector<string> texts = {to_string(std::get<I>(t))...};
	return "(" + join(texts, ", ") + ")";
}
template <class... Args>
string to_string(tuple<Args...> t)
{
	using Tuple = tuple<Args...>;
	return _to_string_tuple(std::forward<Tuple>(t),
							std::make_index_sequence<std::tuple_size<std::decay_t<Tuple>>::value>{});
}
template <class T>
string to_string(vector<T> ar)
{
	vector<string> texts(ar.size());
	for (size_t i = 0; i < ar.size(); ++i)
	{
		texts[i] = to_string(ar[i]);
	}
	return "{" + join(texts, ", ") + "}";
}
template <class T>
string to_string(initializer_list<T> il)
{
	vector<string> texts(il.size());
	size_t i = 0;
	for (T v : il)
	{
		texts[i] = to_string(v);
		i++;
	}
	return "{" + join(texts, ", ") + "}";
}

#ifdef DEBUG_BUILD
#define debugvar(x) debugln(#x, (x))
#define debugvartab(x, t) debugln(tab(t) + #x, (x))
void debug(string name)
{
	std::cerr << name;
}
void debugln(string name)
{
	std::cerr << name << '\n';
}
template <class T>
void debug(string name, T v)
{
	std::cerr << name << " = " << to_string(v);
}
template <class T>
void debugln(string name, T v)
{
	std::cerr << name << " = " << to_string(v) << '\n';
}
template <class T>
void debug(string name, initializer_list<T> il)
{
	std::cerr << name << " = " << to_string(il);
}
template <class T>
void debugln(string name, initializer_list<T> il)
{
	std::cerr << name << " = " << to_string(il) << '\n';
}
template <class... Args>
void debug(string name, Args... args)
{
	std::cerr << name << " = " << to_string(tuple<Args...>(args...));
}
template <class... Args>
void debugln(string name, Args... args)
{
	std::cerr << name << " = " << to_string(tuple<Args...>(args...)) << '\n';
}
#else
#define debugvar(x)
#define debugvartab(x, t)
void debug(string name)
{
}
void debugln(string name) {}
template <class T>
void debug(string name, T v) {}
template <class T>
void debugln(string name, T v) {}
template <class T>
void debug(string name, initializer_list<T> il) {}
template <class T>
void debugln(string name, initializer_list<T> il) {}
template <class... Args>
void debug(string name, Args... args) {}
template <class... Args>
void debugln(string name, Args... args) {}
#endif

#define all(x) (x).begin(), (x).end()
#define pair(a, b) make_pair(a, b)

template <class T>
bool chmax(T &a, const T b)
{
	if (a < b)
	{
		a = b;
		return true;
	}
	return false;
}
template <class T>
bool chmin(T &a, const T b)
{
	if (a > b)
	{
		a = b;
		return true;
	}
	return false;
}
template <class T>
T divup(const T a, const T b)
{
	if (a % b == 0)
	{
		return a / b;
	}
	return a / b + 1;
}
template <class T>
bool cmp_2nd(pair<T, T> a, pair<T, T> b)
{
	if (a.second != b.second)
	{
		return a.second < b.second;
	}
	return a.first < b.first;
}
ll modpow(ll x, ll n, const ll &p)
{
	ll ret = 1;
	while (n > 0)
	{
		if (n & 1)
		{
			(ret *= x) %= p;
		}
		(x *= x) %= p;
		n >>= 1;
	}
	return ret;
}
template <class T>
T modinv(T a, const T &p)
{
	T b = p, u = 1, v = 0;
	while (b)
	{
		T t = a / b;
		a -= t * b;
		swap(a, b);
		u -= t * v;
		swap(u, v);
	}
	u %= p;
	if (u < 0)
	{
		u += p;
	}
	return u;
}
template <class T>
T math_P(T m, T n)
{
	T ret = 1;
	for (T i = m; i > m - n; i--)
	{
		ret *= i;
	}
	return ret;
}
template <class T>
T math_C(T m, T n)
{
	T ret = math_P(m, n);
	for (T i = 2; i <= n; i++)
	{
		ret /= i;
	}
	return ret;
}
ll extended_euclidean(ll u, ll v)
{
	ll r0 = u;
	ll r1 = v;
	ll s0 = 1;
	ll s1 = 0;
	ll t0 = 0;
	ll t1 = 1;
	while (r1 != 0)
	{
		ll q = r0 / r1;
		ll r = r0 - q * r1;
		ll s = s0 - q * s1;
		ll t = t0 - q * t1;
		r0 = r1;
		s0 = s1;
		t0 = t1;
		r1 = r;
		s1 = s;
		t1 = t;
	}
	if (t0 < 0)
	{
		return t0 + u;
	}
	else
	{
		return t0;
	}
}
ll math_C_mod(ll n, ll c, const ll &p)
{
	ll upe = 1;
	ll dow = 1;
	for (ll i = 1; i < c + 1; ++i)
	{
		upe = upe * n % p;
		dow = dow * i % p;
		n -= 1;
	}
	return (upe * extended_euclidean(p, dow)) % p;
}
template <class T>
T math_gcd(T a, T b)
{
	if (b == 0)
	{
		return a;
	}
	else
	{
		return math_gcd(b, a % b);
	}
}
template <class T>
T math_lcm(T a, T b) { return a / math_gcd(a, b) * b; }
template <class T>
T SumStep(T a, T n, T d) { return n * (2 * a + (n - 1) * d) / 2; }
template <class T>
T SumRange(T a, T b, T d) { return SumStep(a, (b - a) / d, d); }

//constexpr ll MOD = 1000000007; // 10^9+7
constexpr ll MOD = 998244353;

/*****/

void Main()
{
	ld A, B, H, M;
	cin >> A >> B >> H >> M;

	ld Ax = cos((H + M / 60) / 12 * M_PI * 2) * A;
	ld Ay = sin((H + M / 60) / 12 * M_PI * 2) * A;
	ld Bx = cos(M / 60 * M_PI * 2) * B;
	ld By = sin(M / 60 * M_PI * 2) * B;
	debugvar(Ax);
	debugvar(Ay);
	debugvar(Bx);
	debugvar(By);

	ld x = Ax - Bx;
	ld y = Ay - By;
	ld ret = sqrt(x * x + y * y);
	cout << ret << endl;
}

/*****/

int main()
{
	std::ios::sync_with_stdio(false);
	std::cin.tie(0);

	std::cout << std::fixed << std::setprecision(10);

	Main();
	std::cerr << flush;
	std::cout << flush;

	return 0;
}