TikTok Delay Minimization

When uploading videos on TikTok, data packets travel through a sequence of n servers (labeled 1, 2, ..., n) before reaching the final server where the video is processed. Each server introduces a delay, represented by delay[i], affecting the overall upload speed.

The upload process begins at a central server (labeled as server 0) and allows data packets to be transmitted across a maximum of k consecutive servers at a time. This means that if a data packet is at server i, it can be transmitted to any server from i+1 to i+k (inclusive).

At each server, the delay specific to that server is added to the total upload time.

To ensure a smooth and efficient upload, calculate the minimum total delay required to reach server n while ensuring that the transmission skips no more than k servers ahead in each step.

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Example
Given:

n = 5  
delay = [1, 4, 2, 6, 2]  
k = 2  

The optimal server path for minimizing upload delay is from server 0 → 1 → 3 → 5.
The total upload delay incurred at servers 1, 3, and 5 is 1 + 2 + 2 = 5, the minimum possible.

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Function Description
Complete the function getMinimumUploadDelay in the editor below.

getMinimumUploadDelay has the following parameters:

• int delay[n]: The delay incurred at each server.
• int k: The maximum allowable skip distance between servers.

Returns

• long: The minimum total delay required to reach the final server.

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Constraints

• 1 ≤ k ≤ n ≤ 5000
• 1 ≤ delay[i] ≤ 10^9

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Input Format for Custom Testing
Given:

n = 6  
delay = [8, 1, 2, 4, 3, 4]  
k = 3  

Output:

6

Explanation:
The optimal path is 0 → 3 → 6.
The total delay is 2 + 4 = 6.

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TikTok Studio Pathways

TikTok's creators are trying to post new content by navigating through a virtual "Studio" represented as a grid. The grid has dimensions n x m, and each cell in the grid represents a section of their Studio, where the creator can add a video, adjust settings, or boost engagement.

However, some sections of the Studio have "content blocks," where the creator is not allowed to make changes or post anything. These are represented by grid sections that are blocked for interaction.

The creator's goal is to navigate from the top-left section of their Studio grid (the initial upload step) to the bottom-right section (the final post step). They can only move in two directions within the Studio:

1. Move one section to the right.
2. Move one section down.

The grid is represented as an array of size n x m, where:

• grid[i][j] = 0 means the section has a "content block" and cannot be used.
• grid[i][j] = 1 means the section is available for interaction.

Determine how many distinct ways the creator can navigate through the Studio to post their content while avoiding any sections that are blocked. Since the number of ways can be very large, return the result modulo 109+710^9 + 7.

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Example
Given:

grid = [
    [1, 1],
    [0, 1]
]

The grid has a "content block" at grid[1][0] = 0. There is only one possible safe path from grid[0][0] to grid[1][1].

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Possible Path

1 1  
0 1  

Thus, the answer is 1 % (10^9 + 7) = 1.

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Function Description
Complete the function countPostPaths in the editor below.

countPostPaths has the following parameter:

• grid[n][m]: a two-dimensional array of integers with n rows and m columns representing the Studio layout.

Returns

• int: The number of distinct paths the creator can take to successfully navigate through the Studio to post content, modulo 109+710^9 + 7.

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Constraints

• 1 ≤ n, m ≤ 1000
• Each cell in the Studio grid contains either a 0 (content block) or a 1 (usable section).

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