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.math.BigDecimal;
import java.math.BigInteger;
import java.math.RoundingMode;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;

public class Main {

  public static void main(String[] args) {
    // abc168_a();
    // abc168_b();
    abc168_c();
    // abc169_a();
    // abc169_b();
    // abc169_c();
    // abc169_d();
    // abc170_a();
    // abc170_b();
    // abc170_c();
    // abc170_d();
    // abc171_a();
    // abc171_b();
    // abc171_c();
    // abc171_d();
    // abc172_a();
    // abc172_b();
    // abc172_c();
    // abc173_a();
    // abc173_b();
    // abc173_c();
  }

  // int 2147483648 [ 2 * 10(9)]
  // long 9223372036854775808 [ 9 * 10(18)]

  public static void abc168_a() {
    try (Scanner sc = new Scanner(System.in)) {
      String n = sc.next();
      Character[] hon = { '2', '4', '5', '7', '9' };
      char[] pon = { '0', '1', '6', '8' };

      for (Character ass : hon) {
        if (ass.equals(n.charAt(n.length() - 1))) {
          System.out.println("hon");
          return;
        }
      }
      for (Character ass : pon) {
        if (ass.equals(n.charAt(n.length() - 1))) {
          System.out.println("pon");
          return;
        }
      }
      System.out.println("bon");
    } catch (Exception e) {
      System.out.println("エラー" + e);
    }
  }

  public static void abc168_b() {
    try (Scanner sc = new Scanner(System.in)) {
      int k = parseI(sc.next());
      String s = sc.next();
      String comma = "...";

      if (s.length() <= k) {
        System.out.println(s);
      } else {
        System.out.println(s.substring(0, k).concat(comma));
      }

    } catch (Exception e) {
      System.out.println("エラー" + e);
    }
  }

  public static void abc168_c() {
    try (Scanner sc = new Scanner(System.in)) {
      int a = parseI(sc.next());
      int b = parseI(sc.next());
      int h = parseI(sc.next());
      int m = parseI(sc.next());

      int hour = h * 60 + m;
      int min = m * 12;

      int ass1 = min <= hour ? hour : min;
      int ass2 = ass1 == hour ? min : hour;

      double deg = ((double) ass1 - ass2);

      deg = 360 < deg ? (deg - 360) / 2 : deg / 2;

      double ans = Math.sqrt(Math.pow(a, 2) + Math.pow(b, 2)
        - (2 * a * b * Math.cos(deg * (Math.PI / 180))));

      System.out.println(ans);

    } catch (Exception e) {
      System.out.println("エラー" + e);
    }
  }

  public static void abc169_a() {
    try (Scanner sc = new Scanner(System.in)) {
      int a = parseI(sc.next());
      int b = parseI(sc.next());
      System.out.println(a * b);
    } catch (Exception e) {
      System.out.println("エラー" + e);
    }
  }

  public static void abc169_b() {
    try (Scanner sc = new Scanner(System.in)) {
      int n = parseI(sc.next());
      Long[] a = new Long[n];

      for (int i = 0; i < n; i++) {
        a[i] = parseL(sc.next());
        if (a[i] == 0L) {
          System.out.println(0);
          return;
        }
      }
      Arrays.sort(a, Collections.reverseOrder());

      BigInteger multiTotal = parseBigI("1");
      for (long value : a) {
        multiTotal = multiTotal.multiply(BigInteger.valueOf(value));
        if (0 < multiTotal.compareTo(parseBigI("1000000000000000000"))) {
          System.out.println(-1);
          return;
        }
      }
      System.out.println(multiTotal);

    } catch (Exception e) {
      e.printStackTrace();
    }
  }

  public static void abc169_c() {
    try (Scanner sc = new Scanner(System.in)) {
      BigDecimal a = parseBigD(sc.next());
      BigDecimal b = parseBigD(sc.next());
      System.out.println(a.multiply(b).setScale(0, RoundingMode.DOWN));
    } catch (Exception e) {
      System.out.println("エラー" + e);
    }
  }

  public static void abc169_d() {
    try (Scanner sc = new Scanner(System.in)) {
      long n = parseL(sc.next());

      long divNum = 0L;
      long ansCnt = 0L;

      while (true) {
        if (divNum == 1) {
          System.out.println(ansCnt);
          return;
        }
      }
    } catch (Exception e) {
      System.out.println("エラー" + e);
    }
  }

  public static void abc170_a() {
    try (Scanner sc = new Scanner(System.in)) {
      int[] x = new int[5];
      int ans = 0;
      for (int i = 0; i < 5; i++) {
        x[i] = parseI(sc.next());
        if (i != 0 && x[i] == 0) {
          ans = x[i - 1] + 1;
        }
      }
      if (ans == 0) {
        ans = x[1] - 1;
      }
      System.out.println(ans);
    } catch (Exception e) {
      System.out.println("エラー" + e);
    }
  }

  public static void abc170_b() {
    try (Scanner sc = new Scanner(System.in)) {
      int body = parseI(sc.next());
      int leg = parseI(sc.next());
      boolean flg = false;

      for (int x = 0; x <= body; x++) {
        if (2 * x + 4 * (body - x) == leg) {
          flg = true;
        }
      }
      System.out.println(flg ? "Yes" : "No");

    } catch (Exception e) {
      System.out.println("エラー" + e);
    }
  }

  public static void abc170_c() {
    try (Scanner sc = new Scanner(System.in)) {
      int x = parseI(sc.next());
      int n = parseI(sc.next());
      List<Integer> p = new ArrayList<Integer>();

      for (int i = 0; i < n; i++) {
        p.add(parseI(sc.next()));
      }
      if (!p.contains(x)) {
        System.out.println(x);
        return;
      }
      for (int i = 1; i <= n / 2 + 1; i++) {
        if (!p.contains(x - i)) {
          System.out.println(x - i);
          break;
        } else if (!p.contains(x + i)) {
          System.out.println(x + i);
          break;
        }
      }
    } catch (Exception e) {
      System.out.println("エラー" + e);
    }
  }

  public static void abc170_d() {
    try (Scanner sc = new Scanner(System.in)) {
      int n = parseI(sc.next());
      int[] a = new int[n];

      int ans = 0;

      for (int i = 0; i < n; i++) {
        a[i] = parseI(sc.next());
      }

      Arrays.sort(a);
      int[] allL = new int[(int) Math.pow(10, 6) + 1];
      Arrays.fill(allL, 0);

      for (int i = 0; i < a.length; i++) {
        if (1 < allL[a[i]]) {
          continue;
        }
        allL[a[i]]++;

        int multiNum = 2;
        while (a[i] * multiNum < allL.length) {
          allL[a[i] * multiNum] += 2;
          multiNum++;
        }
      }

      for (int i = 0; i < a.length; i++) {
        if (allL[a[i]] < 2) {
          ans++;
        }
      }

      System.out.println(ans);

    } catch (Exception e) {
      e.printStackTrace();
    }
  }

  public static void abc171_a() {
    try (Scanner sc = new Scanner(System.in)) {
      String a = sc.next();
      if (Character.isUpperCase(a.charAt(0))) {
        System.out.println("A");
      } else {
        System.out.println("a");
      }
    } catch (Exception e) {
      System.out.println("エラー" + e);
    }
  }

  public static void abc171_b() {
    try (Scanner sc = new Scanner(System.in)) {
      int n = parseI(sc.next());
      int k = parseI(sc.next());

      int[] prices = new int[n];
      for (int i = 0; i < n; i++) {
        prices[i] = parseI(sc.next());
      }
      Arrays.sort(prices);

      int ans = 0;
      while (0 < k) {
        ans += prices[k - 1];
        k--;
      }
      System.out.println(ans);

    } catch (Exception e) {
      System.out.println("エラー" + e);
    }
  }

  public static void abc171_c() {
    try (Scanner sc = new Scanner(System.in)) {

      long number = parseL(sc.next());
      char a = 'a';

      String ans = "";

      long divideCnt = 0;

      divideCnt = (number - 1) / 26;
      ans =
        number % 26 == 0 ? "z" : String.valueOf((char) (a + number % 26 - 1));

      while (true) {
        if (0 == divideCnt) {
          break;
        }
        ans = divideCnt % 26 == 0 ? "z" + ans
          : String.valueOf((char) (a + divideCnt % 26 - 1) + ans);
        divideCnt = (divideCnt - 1) / 26;
      }

      System.out.println(ans);

    } catch (Exception e) {
      System.out.println("エラー" + e);
    }
  }

  public static void abc171_d() {
    try (Scanner sc = new Scanner(System.in)) {

      int chListCnt = parseI(sc.next());
      long[] allNumCnt = new long[(int) Math.pow(10, 5) + 1];
      Arrays.fill(allNumCnt, 0L);

      long sum = 0;

      for (int i = 0; i < chListCnt; i++) {
        int num = parseI(sc.next());
        allNumCnt[num] += 1;
        sum += num;
      }
      int chCnt = parseI(sc.next());
      int[][] beAf = new int[chCnt][2];
      for (int i = 0; i < chCnt; i++) {
        beAf[i][0] = parseI(sc.next());
        beAf[i][1] = parseI(sc.next());
      }

      long diffMultiNum = 0;

      for (int[] changeTarget : beAf) {
        diffMultiNum = allNumCnt[changeTarget[0]];
        if (changeTarget[0] < changeTarget[1]) {
          sum +=
            changeTarget[1] * diffMultiNum - changeTarget[0] * diffMultiNum;
        } else {
          sum -=
            changeTarget[0] * diffMultiNum - changeTarget[1] * diffMultiNum;
        }
        allNumCnt[changeTarget[0]] = 0;
        allNumCnt[changeTarget[1]] += diffMultiNum;
        System.out.println(sum);
      }

    } catch (Exception e) {
      System.out.println("エラー" + e);
    }
  }

  public static void abc172_a() {
    try (Scanner sc = new Scanner(System.in)) {
      int a = parseI(sc.next());

      System.out.println(a + (int) Math.pow(a, 2) + (int) Math.pow(a, 3));
    } catch (Exception e) {
      System.out.println("エラー" + e);
    }
  }

  public static void abc172_b() {
    try (Scanner sc = new Scanner(System.in)) {
      String s = sc.next();
      String t = sc.next();
      int ansCnt = 0;
      for (int i = 0; i < s.length(); i++) {
        if (!parseS(s.charAt(i)).equals(parseS(t.charAt(i)))) {
          ansCnt++;
        }
      }
      System.out.println(ansCnt);

    } catch (Exception e) {
      System.out.println("エラー" + e);
    }
  }

  public static void abc172_c() {
    try (Scanner sc = new Scanner(System.in)) {
      int n = parseI(sc.next());
      int m = parseI(sc.next());
      int k = parseI(sc.next());
      long[] nList = new long[n + 1];
      long[] mList = new long[m + 1];
      nList[0] = 0;
      mList[0] = 0;
      for (int i = 1; i <= n; i++) {
        nList[i] = nList[i - 1] + parseI(sc.next());
      }
      for (int i = 1; i <= m; i++) {
        mList[i] = mList[i - 1] + parseI(sc.next());
      }
      int ansCnt = 0;
      for (int i = 0; i <= n; i++) {
        if (k < nList[i]) {
          break;
        }
        while (k - nList[i] < mList[m])
          m--;
        ansCnt = Math.max(ansCnt, i + m);
      }
      System.out.println(ansCnt);
    }
  }

  public static void abc173_a() {
    try (Scanner sc = new Scanner(System.in)) {
      int payment = parseI(sc.next());
      int max = 10000;
      int thou = 1000;

      System.out.println((max - payment) % thou);
    } catch (Exception e) {
      System.out.println("エラー" + e);
    }
  }

  public static void abc173_b() {
    try (Scanner sc = new Scanner(System.in)) {
      int num = parseI(sc.next());

      // AC
      // WA
      // TLE
      // RE x 0
      int[] ansCount = new int[4];
      final String[] err = { "AC", "WA", "TLE", "RE" };
      Arrays.fill(ansCount, 0);

      for (int i = 0; i < num; i++) {
        String ans = sc.next();
        switch (ans) {
          case "AC":
            ansCount[0]++;
            break;
          case "WA":
            ansCount[1]++;
            break;
          case "TLE":
            ansCount[2]++;
            break;
          case "RE":
            ansCount[3]++;
            break;
        }
      }
      int count = 0;
      for (int answer : ansCount) {
        System.out.println(err[count] + " x " + answer);
        count++;
      }
    } catch (Exception e) {
      System.out.println("エラー" + e);
    }
  }

  public static void abc173_c() {
    try (Scanner sc = new Scanner(System.in)) {
      int row = parseI(sc.next());
      int column = parseI(sc.next());
      int checkBlackCount = parseI(sc.next());
      int existBlack = 0;
      int ansCount = 0;
      int[][] inputList = new int[row][column];
      String input = "";
      for (int i = 0; i < row; i++) {
        input = sc.next();
        for (int x = 0; x < column; x++) {
          inputList[i][x] =
            parseI(parseS(input.charAt(x)).replace(".", "0").replace("#", "1"));
        }
      }

      for (int i = 0; i < (1 << row); i++) {
        for (int x = 0; x < (1 << column); x++) {

          for (int chRownum = 0; chRownum < row; chRownum++) {
            for (int chColNum = 0; chColNum < column; chColNum++) {
              if (inputList[chRownum][chColNum] == 1
                && ((i >> chRownum) & 1) == 0 && ((x >> chColNum) & 1) == 0) {
                existBlack++;
              }
            }
          }
          if (existBlack == checkBlackCount) ansCount++;
          existBlack = 0;

        }
      }
      System.out.println(ansCount);

    } catch (Exception e) {
      System.out.println("エラー" + e);
    }
  }

  public static int parseI(String value) {
    return Integer.parseInt(value);
  }

  public static long parseL(String value) {
    return Long.parseLong(value);
  }

  public static double parseD(String value) {
    return Double.parseDouble(value);
  }

  public static <T> String parseS(T value) {
    return String.valueOf(value);
  }

  public static BigDecimal parseBigD(String value) {
    return new BigDecimal(value);
  }

  public static BigInteger parseBigI(String value) {
    return new BigInteger(value);
  }

}