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)

/*  4_2
    Y_Aizaki    */

#include <stdio.h>
#include <math.h>
#define PI 3.14159265359

/* プロトタイプ宣言 */
double radian(double hour_date, double minute_date);
double handDistance(double rad_date, double len_date1, double len_date2);

int main(void){
    double len_hour, len_minute, hour, minute;
    // 時針の長さ、分針の長さ、~時、~分
    scanf("%lf%lf%lf%lf", &len_hour, &len_minute, &hour, &minute);

    double rad;
    // 針間の角度
    rad = radian(hour, minute);

    double ans;
    // answer
    ans = handDistance(rad, len_hour, len_minute);
    printf("%.10f\n", ans);

    return 0;

}

double radian(double hour_date, double minute_date){
    double rad_hour, rad_minute, rad;

    rad_hour = (PI / 6.0) * hour_date + (PI / 360.0) * minute_date;
    rad_minute = (PI / 30.0) * minute_date;
    rad = rad_hour - rad_minute;
    
    return rad;
    // radが負であったり、PIより大きい場合もあるが、後の余弦定理で用いる点で支障はない

}

double handDistance(double rad_date, double len_date1, double len_date2){
    double distance;
    distance = sqrt(pow(len_date1, 2.0) + pow(len_date2, 2.0) - 2.0 * len_date1 * len_date2 * cos(rad_date));

    return distance;
}