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: Wrong Answer)

// CPP program to find third 
// side of triangle using 
// law of cosines 

#include <bits/stdc++.h> 
using namespace std; 

int min(int a, int b) 
{ 
  return (a < b)? a:b; 
  
} 
int calculateangle(double H, double M) 
{ 
  // validate 
  if (H <0 || M < 0 || H >12 || M > 60) 
    cout<<"input is wrong "; 
  if (H == 12) 
      H = 0; 
  if (M == 60) 
      M = 0; 
  // Calculate the angles 
  int hourangle = 0.5 * (H * 60 + M); 
  int minangle = 6 * M; 
  // Find the difference  
  int angdiff = abs(hourangle - minangle); 
  // Return the smaller angle of two possible angles 
  angdiff = min(360 - angdiff, angdiff); 
  return angdiff; 
} 

// Function to calculate cos value of angle c 
float cal_cos(float n) 
{ 
	float accuracy = 0.0001, x1, denominator, cosx, cosval; 

	// Converting degrees to radian 
	n = n * (3.142 / 180.0); 

	x1 = 1; 

	// Maps the sum along the series 
	cosx = x1; 

	// Holds the actual value of sin(n) 
	cosval = cos(n); 
	int i = 1; 
	do { 
		denominator = 2 * i * (2 * i - 1); 
		x1 = -x1 * n * n / denominator; 
		cosx = cosx + x1; 
		i = i + 1; 
	} while (accuracy <= fabs(cosval - cosx)); 

	return cosx; 
} 

// Function to find third side 
float third_side(int a, int b, float c) 
{ 
	float angle = cal_cos(c); 
	return sqrt((a * a) + (b * b) - 2 * a * b * angle); 
} 
// Driver program to check the above function 
int main() 
{ 
	
	int a, b, h, m;
	cin >> a >> b >> h >> m;


	// function call 
	cout << setprecision(3) << fixed << third_side(a, b, (double)calculateangle(h, m)) << "\n";

	return 0; 
}