You are given a 0-indexed array of `n` integers `differences`, which describes the differences between each pair of consecutive integers of a hidden sequence of length `(n + 1)`. More formally, call the hidden sequence `hidden`, then we have that `differences[i] = hidden[i + 1] - hidden[i]`.

You are further given two integers `lower` and `upper` that describe the inclusive range of values `[lower, upper]` that the hidden sequence can contain.

- For example, given `differences = [1, -3, 4]`, `lower = 1`, `upper = 6`, the hidden sequence is a sequence of length `4` whose elements are in between `1` and `6` (inclusive).
  - `[3, 4, 1, 5]` and `[4, 5, 2, 6]` are possible hidden sequences.
  - `[5, 6, 3, 7]` is not possible since it contains an element greater than `6`.
  - `[1, 2, 3, 4]` is not possible since the differences are not correct.

Return the number of possible hidden sequences there are. If there are no possible sequences, return `0`.

Example 1:

    Input: differences = [1,-3,4], lower = 1, upper = 6
    Output: 2
    Explanation: The possible hidden sequences are:
    - [3, 4, 1, 5]
    - [4, 5, 2, 6]
    Thus, we return 2.

Example 2:

    Input: differences = [3,-4,5,1,-2], lower = -4, upper = 5
    Output: 4
    Explanation: The possible hidden sequences are:
    - [-3, 0, -4, 1, 2, 0]
    - [-2, 1, -3, 2, 3, 1]
    - [-1, 2, -2, 3, 4, 2]
    - [0, 3, -1, 4, 5, 3]
    Thus, we return 4.

Example 3:

    Input: differences = [4,-7,2], lower = 3, upper = 6
    Output: 0
    Explanation: There are no possible hidden sequences. Thus, we return 0.

Constraints:

- `n == differences.length`
- `1 <= n <= 105`
- `-105 <= differences[i] <= 105`
- `-105 <= lower <= upper <= 105`