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# Subarray Cost Sum

Problem Description

Let's the sum of the array S be sum(S) and the maximum be max(S). The cost of an array S is ceil(sum(S)/2) * max(S). ceil(x) is the smallest integer not less than x.

You have an array A of length N. Find the sum of the cost of all the subarrays of this array.

Since the answer can be large, return it modulo 10+ 7.

Problem Constraints

1 <= N <= 5 x 105

1 <= A[i] <= 106

Input Format

The first and only argument contains an integer array A of length N.

Output Format

Return the sum of cost of all subarrays modulo 10+ 7.

Example Input

Input 1:

```  A : [ 1, 2 ]
```

Input 2:

```  A : [5]
```

Example Output

Output 1:

```  7
```

Output 2:

```  15
```

Example Explanation

Explanation 1:

```  The array has 3 subarrays-
1. [1] - Cost = 1 * ceil(1/2) = 1
2. [2] - Cost = 2 * ceil(2/2) = 2
3. [1, 2] - Cost = 2 * ceil(3/2) = 4
Sum of cost = 7
```

Explanation 2:

```  It has only one subarray. Cost is 5 * ceil(5/2) = 15
```

NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a question? Checkout Sample Codes for more details.
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