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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.math.BigInteger;
import java.util.*;
import java.io.*;
import java.text.*;

public class Main {
    static BufferedReader br = new BufferedReader(new InputStreamReader(System.in), 32768);
    static PrintWriter out = new PrintWriter(System.out);
    static StringTokenizer t;

    static String sn() {
        while (t == null || !t.hasMoreTokens()) {
            try {
                t = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                throw new RuntimeException();
            }
        }
        return t.nextToken();
    }

    static int ni() {
        return Integer.parseInt(sn());
    }

    static long nlo() {
        return Long.parseLong(sn());
    }

    public static void main(String args[]) {
        int t = 1;
        while (t-- > 0) {
            solve();
        }
        out.close();
    }

    static long mod = (long) 998244353;

    static long pro(long a, long b) {
        return (a % mod * b % mod) % mod;
    }

    static long add(long a, long b) {
        return (a + b) % mod;
    }

    static long sub(long a, long b) {
        return ((a % mod - b % mod) + mod) % mod;
    }

    static int maxn = 1000005;

    static int pow(int n) {
        return (int) (Math.log10(n) / Math.log10(2));
    }

    static long modpow(long x, long y) {
        long res = 1l;
        x %= mod;
        while (y > 0) {
            if (y % 2 != 0)
                res = pro(res, x);
            x = pro(x, x);
            y /= 2;
        }
        return res;
    }

    static class pair {
        String a;
        int b;

        pair(String x, int y) {
            a = x;
            b = y;
        }
    }

    static long modInverse(long n) {
        BigInteger n1 = new BigInteger(Long.toString(n));
        String s = (n1.modInverse(new BigInteger(Long.toString(mod)))).toString();
        return Long.parseLong(s);
    }

    static boolean v[] = new boolean[1000005];

    static void seive() {
        v[1] = true;
        for (int i = 2; i < 1000005; i++) {
            if (!v[i]) {
                for (int j = 2 * i; j < 1000005; j += i)
                    v[j] = true;
            }
        }
    }

    static boolean isprime(long n) {
        if (n == 1)
            return false;
        for (int i = 2; i * i <= n; i++) {
            if (n % i == 0)
                return false;
        }
        return true;
    }

    static long gcd(long a, long b) {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }
    static DecimalFormat df=new DecimalFormat("0.000000000000000000000");
    static void solve() {
        int a = ni();
        int b = ni();
        int h = ni();
        int m = ni();
        double alpha = (30.0 * h) - ((11.0 * m) / 2.0);
//        out.println(Math.cos(Math.toRadians(270)));
        double ans = Math.sqrt(a * a + b * b - 2 * a * b * Math.cos(Math.toRadians(alpha)));
        out.println(df.format(ans));
    }
}