Building Hops

You are given a sequence of buildings with heights \(h_1, h_2, \ldots, h_n\). Starting from the first building, you want to determine whether you can reach the last building by performing consecutive jumps. A jump from building \(i\) to building \(i+1\) is allowed if and only if

\(h_{i+1} \le h_i + k\)

where \(k\) is a given non-negative integer representing the maximum allowable increase in height for a jump. If the sequence of jumps from the first to the last building is feasible, output True; otherwise, output False.

Note: If there are no buildings, it is impossible to reach the last building.

inputFormat

The input is given via standard input (stdin) in the following format:

1. An integer \(n\) representing the number of buildings.
2. If \(n > 0\), a line of \(n\) space-separated integers denoting the heights of the buildings.
3. An integer \(k\), the maximum allowed height difference for a single jump.

If \(n = 0\), the line of building heights may be omitted.

outputFormat

Output a single line to standard output (stdout) containing either True or False, indicating whether it is possible to reach the last building from the first one.

5
1 2 3 4 5
2

True