Contest Duration: - (local time) (120 minutes) Back to Home
C - Max Dot /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

• 0 \leq x_1 \leq x_2 \leq \cdots \leq x_N \leq M
• \sum_{1 \leq i \leq N} x_i=S

ここで，x のスコアを \sum_{1 \leq i \leq N} A_i \times x_i と定義します． x のスコアとしてありうる最大の値を求めてください．

### 制約

• 1 \leq N \leq 5000
• 1 \leq M \leq 10^6
• 1 \leq S \leq \min(N \times M,10^6)
• 1 \leq A_i \leq 10^6
• 入力される値はすべて整数である

### 入力

N M S
A_1 A_2 \cdots A_N


### 入力例 1

3 2 3
1 2 3


### 出力例 1

8.00000000000000000000


x=(0,1,2) とするのが最適です．

### 入力例 2

3 3 2
5 1 1


### 出力例 2

4.66666666666666666667


x=(2/3,2/3,2/3) とするのが最適です．

### 入力例 3

10 234567 1000000
353239 53676 45485 617014 886590 423581 172670 928532 312338 981241


### 出力例 3

676780145098.25000000000000000000


Score : 600 points

### Problem Statement

Given are integers N, M, S, and a sequence of N integers A=(A_1,A_2,\cdots,A_N).

Consider making a sequence of N non-negative real numbers x=(x_1,x_2,\cdots,x_N) satisfying all of the following conditions:

• 0 \leq x_1 \leq x_2 \leq \cdots \leq x_N \leq M,
• \sum_{1 \leq i \leq N} x_i=S.

Now, let us define the score of x as \sum_{1 \leq i \leq N} A_i \times x_i. Find the maximum possible score of x.

### Constraints

• 1 \leq N \leq 5000
• 1 \leq M \leq 10^6
• 1 \leq S \leq \min(N \times M,10^6)
• 1 \leq A_i \leq 10^6
• All values in input are integers.

### Input

Input is given from Standard Input in the following format:

N M S
A_1 A_2 \cdots A_N


### Constraints

Print the answer. Your output will be considered correct if its absolute or relative error is at most 10^{-6}.

### Sample Input 1

3 2 3
1 2 3


### Sample Output 1

8.00000000000000000000


The optimal choice is x=(0,1,2).

### Sample Input 2

3 3 2
5 1 1


### Sample Output 2

4.66666666666666666667


The optimal choice is x=(2/3,2/3,2/3).

### Sample Input 3

10 234567 1000000
353239 53676 45485 617014 886590 423581 172670 928532 312338 981241


### Sample Output 3

676780145098.25000000000000000000