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)


#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <cmath>
#include <climits>
#include <cassert>
#include <iostream>
#include <algorithm>
#include <map>
#include <set>
#include <stack>
#include <queue>
#include <string>
#include <list>
#include <bitset>
#include <vector>
using namespace std;

#define I64d_OJ

//#ifdef I64d_OJ
//#define LL __int64
//#endif // I64d_OJ
#ifdef I64d_OJ
#define LL long long
#endif // I64d_OJ

typedef unsigned LL ULL;
typedef unsigned uint;
typedef pair<int,int> pii;
typedef pair<double,double> pdd;
typedef pair<LL,LL> pLL;
typedef vector<int> vi;

inline int read(){
    int x=0,f=1;
    char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-') f=-f; ch=getchar();}
    while(ch>='0'&&ch<='9'){x=x*10+ch-'0'; ch=getchar();}
    return x*f;
}

#define lson l,mid,rt<<1
#define rson mid+1,r,rt<<1|1
#define ls rt<<1
#define rs rt<<1|1
#define MID(a,b) (((LL)(a)+(LL)(b))>>1)
#define absx(a) ((a)<0?-(a):(a))
#define MK(a,b) make_pair(a,b)
#define PB(a) push_back(a)
#define lowbit(x) ((x)&-(x))

#define lc c[x][0]
#define rc c[x][1]

template< typename T >
inline void Max(T &a,T &b){if(a<b) a=b;}
template< typename T>
inline void Min(T &a,T &b){if(a>b) a=b;}

const double pi=(double)acos(-1.0);
const double eps=(double)1e-8;
const int INF = (int) 0x3f3f3f3f;
const int MOD = (int) 1e9+7;
const int MAXN =(int) 2e5+10;
const int MAXM = (int) 3e6+10;

///--------------------START-------------------------
int A,B,H,M;

void work(){
    scanf("%d%d%d%d",&A,&B,&H,&M);
//    printf("H = %d, M=%d\n",H,M);
    double theta = 2*pi*(H*1.0/12+M*1.0/60/12-M*1.0/60);
    if(theta<0) theta=theta*(-1.0);
    if(theta>pi) theta = 2.0*pi-theta;
//    printf("theta = %lf\n",theta/2/pi*360);
    double ans=A*1.0*A+B*1.0*B-2.0*A*B*cos(theta);
    printf("%.12lf\n",sqrt(ans));
}

///--------------------END-------------------------
int main(){
#ifdef NNever
//freopen("data.in","r",stdin);
///freopen("out.txt","w",stdout);
#endif // NNever
    work();
    return 0;
}