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
ryo_1129*/
#include<stdio.h>
#include<math.h>
//プロトタイプ宣言
double distance(int length_hour,int length_minute,double rad);

int main(void){
    //変数宣言
    int A,B,hour,minute;
    double radhour,radminute,rad,length;
    //入力
    scanf("%d %d %d %d",&A,&B,&hour,&minute);
    //演習率πを決める。
    const double pi = 3.14159265358979;
    //時針、分針を求める。
    radminute = 2*pi*minute/60;
    radhour = 2*pi*(hour*60+minute)/720;
    //角度の差を求める。cos(θ)=cos(-θ)に注意
    rad = radhour - radminute;
    //長さを求める。関数の呼び出し
    length = distance(A,B,rad);
    //出力
    printf("%.9f\n",length);
    return 0;
}
//時針と分針の長さと角度から端点間の長さを求める。引数、時針の長さ、分針の長さ、それらのなす角度
double distance(int length_hour,int length_minute,double rad){
    double length;//変数宣言
    //余弦定理を用いて端点間の長さを求める
    length = sqrt(pow(length_hour,2)+pow(length_minute,2)-2*length_hour*length_minute*cos(rad));
    // 端点間の長さを返す
    return length;
}