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: Wrong Answer)

import java.io.*;
import java.util.*;

class Main{
    final static long INF = Long.MAX_VALUE / 2;
    final static int MOD = 1_000_000_007;
    final static int SIZE = 1_000_000;
    long[] fac = new long[SIZE];
    long[] inv = new long[SIZE];
    long[] finv = new long[SIZE];
    FastScanner sc = new FastScanner();

    public static void main(String[] args) {
        new Main().solve();
    }

    void solve(){

        int a = sc.nextInt();
        int b = sc.nextInt();
        int h = sc.nextInt();
        int m = sc.nextInt();

        double a_d = Math.min(h * 30.0 + m / 60.0 * 30.0, 180.0 - (h * 30.0 + m / 60.0 * 30.0));
        double b_d = Math.min(m * 6.0, 180.0 - m * 6.0);
        double a_x = a * Math.sin(Math.toRadians(a_d));
        double a_y = a * Math.cos(Math.toRadians(a_d));
        double b_x = b * Math.sin(Math.toRadians(b_d));
        double b_y = b * Math.cos(Math.toRadians(b_d));

        System.out.println(String.format("%.15f", Math.sqrt((a_x - b_x) * (a_x - b_x) + (a_y - b_y) * (a_y - b_y))));

    }

    long gcd(long a, long b){ // return aとbの最大公約数
        if(b == 0){
          return a;
        }
        return gcd(b, a % b);
    }

    long lcm(long a, long b){ // return aとbの最小公倍数
        return a * b / gcd(a, b);
    }

    long inv(long a){ // return aの逆元 (mod MOD)
        return pow(a, MOD - 2);
    }

    long pow(long a, long r){ // return a^r (mod MOD)
        long sum = 1;
        while(r > 0){
            if((r & 1) == 1){ // 2進数表記で末尾1の時
                sum *= a;
                sum %= MOD;
            }
            a *= a;
            a %= MOD;
            r >>= 1;
        }
        return sum;
    }

    long modFact(long n){ // retur n! (mod MOD)
        if(n == 0){
            return 1;
        }
        return n * modFact(n - 1) % MOD;
    }

    long fact(long n){ // return n!
        if(n == 0){
            return 1;
        }
        return n * fact(n - 1);
    }

    void initCOMB(){
        fac[0] = fac[1] = 1;
        inv[1] = 1;
        finv[0] = finv[1] = 1;
        for(int i = 2; i < SIZE; i++){
            fac[i] = fac[i - 1] * i % MOD;
            inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
            finv[i] = finv[i - 1] * inv[i] % MOD;
        }
    }

    long modComb(int n, int r){ // return nCr (先にinitCOMB()必要)
        if(n < r || n < 0 || r < 0) return 0;
        return fac[n] * finv[r] % MOD * finv[n - r] % MOD;
    }

    long comb(long n, long r){ // return nCr
        long num = 1;
        for(long i = 1; i <= r; i++){
            num = num * (n - i + 1) / i;
        }
        return num;
    }

    boolean isPrime(long a){ // aの素数判定
        if(a <= 1) return false;
        for(int i = 2; i * i <= a; i++){
            if(a % i == 0) return false;
        }
        return true;
    }

    int lowerBound(long[] a, long v){ // return 配列a内のv以上の要素の内最低の要素のイテレータ
        int r = a.length;
        int l = -1;
        while(r - l > 1){
            int mid = (r + l) / 2;
            if(a[mid] >= v){
                r = mid;
            }else{
                l = mid;
            }
        }
        return r;
    }

    int upperBound(long[] a, long v){ // return 配列a内のvより大きい要素の内最低の要素のイテレータ
        int r = a.length;
        int l = -1;
        while(r - l > 1){
            int mid = (r + l) / 2;
            if(a[mid] > v){
                r = mid;
            }else{
                l = mid;
            }
        }
        return r;
    }

    String nextPermutation(String s){ // return sの次の順列
        ArrayList<Character> list = new ArrayList<>();
        for(int i = 0; i < s.length(); i++) list.add(s.charAt(i));

        int pivotPos = -1;
        char pivot = 0;
        for(int i = list.size() - 2; i >= 0; i--){
            if(list.get(i) < list.get(i+1)){
    			pivotPos = i;
    			pivot = list.get(i);
    			break;
    		}
    	}

        if(pivotPos == -1 && pivot == 0) return null;

        int L = pivotPos + 1;
        int R = list.size() - 1;
    	int minPos = -1;
    	char min = Character.MAX_VALUE;
    	for(int i = R; i >= L; i--){
    		if(pivot < list.get(i)){
    			if(list.get(i) < min){
    				min = list.get(i);
    				minPos = i;
    			}
    		}
    	}

    	Collections.swap(list, pivotPos, minPos);
    	Collections.sort(list.subList(L, R + 1));

    	StringBuilder sb = new StringBuilder();
    	for(int i=0; i<list.size(); i++) sb.append(list.get(i));

    	return sb.toString();
    }

    boolean nextPermutation(long[] a){
        for(int i = a.length - 1; i > 0; i--){
            if(a[i - 1] < a[i]){
                int swapIndex = find(a[i - 1], a, i, a.length - 1);
                long temp = a[swapIndex];
                a[swapIndex] = a[i - 1];
                a[i - 1] = temp;
                Arrays.sort(a, i, a.length);
                return true;
            }
        }
        return false;
    }

    int find(long dest, long[] a, int s, int e){
        if(s == e){
            return s;
        }
        int m = (s + e + 1) / 2;
        return a[m] <= dest ? find(dest, a, s, m - 1) : find(dest, a, m, e);
    }

    void elimination(int[][] a, int[] b) {
        int n = a.length;
        double f;
        for(int k = 0; k < n - 1; k++){
            for(int i = k + 1; i < n; i++){
                f = - a[i][k] / a[k][k];
                for(int j = k + 1; j < n; j++){
                    a[i][j] += f * a[k][j];
                }
                b[i] += f * b[k];
            }
            for(int i = n - 1; i >= 0; i--){
                for(int j = i + 1; j < n; j++){
                    b[i] -= a[i][j] * b[j];
                }
                b[i] = b[i] / a[i][i];
            }
        }
   }



   class SegmentTree{

       //------------------------------------------------------------
       // 2 * n - 1 : 木全体のノード数
       // i + n - 1 : 配列のi番目が対応するノードの番号
       // 2 * i + 1, 2 * i + 2 : i番目のノードの子ノードの番号
       // (i - 1) / 2 : i番目のノードの親ノードの番号
       //
       // int n = sc.nextInt();
       // long[] a = new long[n];
       // for(int i = 0; i < n; i++) a[i] = sc.nextLong();
       // SegmentTree st = new SegmentTree(a);
       // int l = sc.nextInt() - 1;
       // int r = sc.nextInt() - 1;
       // System.out.println(st.query(l, r));
       //------------------------------------------------------------

       final static long INF = Long.MAX_VALUE / 2;

       // long e = INF; // 単位元
       long e = 0;
       long func(long a, long b){ // 処理
           // return Math.min(a, b);
           return a + b;
       }

       int n; // 配列の要素数を超える最小の2のべき乗
       long[] node;

       SegmentTree(long[] a){
           init(a);
       }

       void init(long[] a){ // 配列aで初期化
           n = 1;
           while(n < a.length){
               n *= 2;
           }
           node = new long[2 * n - 1];
           Arrays.fill(node, e);
           for(int i = 0; i < a.length; i++){
               node[i + n - 1] = a[i];
           }
           for(int i = n - 2; i >= 0; i--){
               node[i] = func(node[2 * i + 1], node[2 * i + 2]);
           }
       }

       void update(int p, long v){ // 配列のp番目をvに変更し、木全体を更新
           p = p + n - 1;
           node[p] = v;
           while(p > 0){
               p = (p - 1) / 2;
               node[p] = func(node[2 * p + 1], node[2 * p + 2]);
           }
       }

       long query(int a, int b){ // 区間[a, b)についてクエリを処理
           return query(a, b, 0, 0, n);
       }

       long query(int a, int b, int k, int l, int r){
           if(r <= a || b <= l) return e;
           if(a <= l && r <= b) return node[k];
           return func(query(a, b, 2 * k + 1, l, (l + r) / 2), query(a, b, 2 * k + 2, (l + r) / 2, r));
       }

   }



}



class Pair implements Comparable<Pair>{
    long a, b;
    public Pair(long i, long j){
        a = i;
        b = j;
    }

    @Override
    public int compareTo(Pair p){
        if(this.b < p.b) return -1;
        else if(this.b > p.b) return 1;
        else return 0;
    }
}



class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    private boolean hasNextByte(){
        if(ptr < buflen){
            return true;
        }else{
            ptr = 0;
            try{
                buflen = in.read(buffer);
            }catch(IOException e){
                e.printStackTrace();
            }
            if(buflen <= 0){
                return false;
            }
        }
        return true;
    }
    private int readByte(){
        if(hasNextByte()) return buffer[ptr++];
        else return -1;
    }
    private static boolean isPrintableChar(int c){
        return 33 <= c && c <= 126;
    }
    public boolean hasNext(){
        while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
        return hasNextByte();
    }
    public String next(){
        if(!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while(isPrintableChar(b)){
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    public long nextLong(){
        if(!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if(b == '-'){
            minus = true;
            b = readByte();
        }
        if(b < '0' || '9' < b){
            throw new NumberFormatException();
        }
        while(true){
            if('0' <= b && b <= '9'){
                n *= 10;
                n += b - '0';
            }else if(b == -1 || !isPrintableChar(b)){
                return minus ? -n : n;
            }else{
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }
    public int nextInt(){
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
        return (int) nl;
    }
    public double nextDouble(){
        return Double.parseDouble(next());
    }
}