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)

/* ex4_2: Colon
    Jun_JPN */

#include <stdio.h>
#include <math.h>

int main(void){

    double s_hand, l_hand, hour, min, rad, length;

    scanf("%lf %lf %lf %lf", &s_hand, &l_hand, &hour, &min);

    /* 長針と短針のなす角radを計算
        0時方向ベクトルと長針がなす偏角theta1は(min/60)*2*M_PI
        0時方向ベクトルと短針がなす偏角theta2は(hour/12)*2*M_PI + (min/60)*(1/12)*2*M_PI
        よって，rad = |theta1-theta2|である */
    rad = fabs(60*hour - 11*min)/360 * M_PI;    //fabs関数はdouble型の絶対値をとる関数

    /* 余弦定理で求める長さlengthを計算
        なす角の大きさが0，M_PIラジアンのときは余弦定理が使えないので注意 */
    if (rad == 0){
        length = l_hand - s_hand;
    } else if (rad == M_PI){
        length = l_hand + s_hand;
    } else{
        length = sqrt(l_hand*l_hand + s_hand*s_hand - 2*l_hand*s_hand*cos(rad));    //余弦定理
    }

    printf("%lf\n", length);

    return 0;
}