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)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#define SIZE 100
#define rep(i, N) for (i = 0; i < N; i++) //制御変数iを用いてN回転
#define array(N, t) (t*)calloc(N, sizeof(t)) //t型N要素の1次元配列を動的確保後0クリア(freeを忘れずに)
#define zero(a); {int iter; rep(iter, sizeof(a)/sizeof((a)[0])) (a)[iter]=0;} //1次元配列aのゼロ初期化?
typedef long long ll;
void print_log(); //とりあえず文字を出力してどこまで実行できているか確認(for debug)
void printa_int(int *a, int size); //int型の1次元配列aを出力(for debug)

int main() {
    long A, B, H, M;
    long double angle, ans;
    scanf("%ld %ld %ld %ld", &A, &B, &H, &M);
    angle = 30.0 * H - 5.5 * M;
    if (angle > 180.0) angle -= 180.0;
    else if (angle < -180.0) angle += 180.0;
    ans = sqrtl(A * A + B * B - 2.0 * A * B * cosl(angle * acosl(-1.0) / 180.0));
    printf("%.20llf\n", ans);
    return 0;
}

void print_log() {
    printf("===finish!===\n");
}

void printa_int(int *a, int size) {
    int i;
    printf("[");
    for (i = 0; i < size; i++)
        printf("%d, ", a[i]);
    printf("]\n");
}