C - : (Colon) /

### 問題文

0 時ちょうどに時針と分針は重なっていました。ちょうど HM 分になったとき、2 本の針の固定されていない方の端点は何センチメートル離れているでしょうか。

### 制約

• 入力はすべて整数
• 1 \leq A, B \leq 1000
• 0 \leq H \leq 11
• 0 \leq M \leq 59

### 入力

A B H M


### 入力例 1

3 4 9 0


### 出力例 1

5.00000000000000000000


2 本の針は図のようになるので、答えは 5 センチメートルです。

### 入力例 2

3 4 10 40


### 出力例 2

4.56425719433005567605


2 本の針は図のようになります。各針は常に一定の角速度で回ることに注意してください。

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.