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)

/* ex4_2
   moka223711 */

#include <stdio.h>
#include <math.h>
#define PI 3.14159265358

int main(void){
    // 時針の長さがlenh[cm]、分針の長さがlenm[cm]である時計のhour時minute分における
    // 時針の先端と分針の先端の距離を求める
    
    double lenh, lenm, hour, minute, radh, radm, rad, ans;
    scanf("%lf %lf %lf %lf", &lenh, &lenm, &hour, &minute);
    
    // 針が12時を指しているときを0[rad]とする
    // 時針は12時間(12*60分)で一周するので、hour時minute分のとき
    // 時針の角度radhは、2*PIに(hour/12+minute/60/12)をかけたものになる
    // 分針は60分で一周するので、分針の角度radmは2*PIにminute/60をかけたものになる
    radh = 2 * PI * (hour + minute / 60) / 12;
    radm = 2 * PI * minute / 60;
    
    // なす角を知りたいのでPI(180°)より小さい方を選ぶ
    rad = (radh-radm < PI) ? radh-radm : radm-radh;
    
    // 余弦定理を用いて時針の先端と分針の先端の距離を求める
    ans = sqrt(pow(lenh, 2) + pow(lenm, 2) - 2*lenh*lenm*cos(rad));
    // 誤差は10^{-9}まで許されるので10^{-10}まで表示する
    printf("%.10lf", ans);
    
    return 0;
}