Block Adventure
Contest: Codeforces Round 578 (Div. 2)
Difficulty rating: 1200
Tags: dp, greedy

Gildong is playing a video game called Block Adventure. In Block Adventure, there are $$$n$$$ columns of blocks in a row, and the columns are numbered from $$$1$$$ to $$$n$$$. All blocks have equal heights. The height of the $$$i$$$-th column is represented as $$$h_i$$$, which is the number of blocks stacked in the $$$i$$$-th column.

Gildong plays the game as a character that can stand only on the top of the columns. At the beginning, the character is standing on the top of the $$$1$$$-st column. The goal of the game is to move the character to the top of the $$$n$$$-th column.

The character also has a bag that can hold infinitely many blocks. When the character is on the top of the $$$i$$$-th column, Gildong can take one of the following three actions as many times as he wants:

- if there is at least one block on the column, remove one block from the top of the $$$i$$$-th column and put it in the bag;
- if there is at least one block in the bag, take one block out of the bag and place it on the top of the $$$i$$$-th column;
- if $$$i < n$$$ and $$$|h_i - h_{i+1}| \le k$$$, move the character to the top of the $$$i+1$$$-st column. $$$k$$$ is a non-negative integer given at the beginning of the game. Note that it is only possible to move to the next column.

In actions of the first two types the character remains in the $$$i$$$-th column, and the value $$$h_i$$$ changes.

The character initially has $$$m$$$ blocks in the bag. Gildong wants to know if it is possible to win the game. Help Gildong find the answer to his question.

Input format:
Each test contains one or more test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 1000$$$). Description of the test cases follows.

The first line of each test case contains three integers $$$n$$$, $$$m$$$, and $$$k$$$ ($$$1 \le n \le 100$$$, $$$0 \le m \le 10^6$$$, $$$0 \le k \le 10^6$$$) — the number of columns in the game, the number of blocks in the character's bag at the beginning, and the non-negative integer $$$k$$$ described in the statement.

The second line of each test case contains $$$n$$$ integers. The $$$i$$$-th integer is $$$h_i$$$ ($$$0 \le h_i \le 10^6$$$), the initial height of the $$$i$$$-th column.

Output format:
For each test case, print "YES" if it is possible to win the game. Otherwise, print "NO".

You can print each letter in any case (upper or lower).

Constraints:
Time limit: 1.0 s
Memory limit: 256.0 MB

Note:
In the first case, Gildong can take one block from the $$$1$$$-st column, move to the $$$2$$$-nd column, put the block on the $$$2$$$-nd column, then move to the $$$3$$$-rd column.

In the second case, Gildong has to put the block in his bag on the $$$1$$$-st column to get to the $$$2$$$-nd column. But it is impossible to get to the $$$3$$$-rd column because $$$|h_2 - h_3| = 3 > k$$$ and there is no way to decrease the gap.

In the fifth case, the character is already on the $$$n$$$-th column from the start so the game is won instantly.

Example input:
5
3 0 1
4 3 5
3 1 2
1 4 7
4 10 0
10 20 10 20
2 5 5
0 11
1 9 9
99

Example output:
YES
NO
YES
NO
YES

Editorial:
We can easily see that it's always optimal to have as many blocks as possible in the bag before getting to the next column. Therefore, if the character is currently on the top of the $$$i$$$-th column, Gildong just needs to make $$$h_i$$$ become $$$max(0, h_{i+1} - k)$$$ by repeating the $$$1$$$-st or the $$$2$$$-nd action. In other words, we should add $$$h_i - max(0, h_{i+1} - k)$$$ blocks to the bag. Adding or subtracting one by one will lead to TLE. If there exists a situation where the bag will have negative number of blocks, the answer is NO. Otherwise the answer is YES.
Time complexity: $$$O(n)$$$ for each test case.