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Finally a monsoon has come. According to the Meteorological Department, there will be rain in the upcoming N days in the city. Initially, the water level of the city is zero millimetres. The amount of rain on the i-th day can be described by an integer A_{i} as follows:
If A_{i} > 0, the water level of the city increases by A_{i} millimetres on the i-th day.
If A_{i} = 0, there is no rain on the i-th day. The water level of the city decreases by D millimetres on such a day. However, if the water level is less than D millimetres before the i-th day, then it becomes zero instead.

There will be a red alert in the city if the water level becomes strictly greater than H millimetres on at least one of the N days. Determine if there will be a red alert.

------ Input Format ------

• The first line of the input contains a single integer T denoting the number of test cases. The description of T test cases follows.
• The first line of each test case contains three space-separated integers N, D and H.
• The second line contains $N space-separated integers A_{1}, A_{2}, \ldots, A_{N}$.

------ Output Format ------

For each test case, print a single line containing the string "YES" if there will be a red alert or "NO" otherwise.

------ Constraints ------

$1 ≤ T ≤ 10^{3}$
$1 ≤ N, D ≤ 10^{2}$
$0 ≤ A_{i} ≤ 10^{2}$ for each valid $i$
$1 ≤ H ≤ 10^{4}$

------ subtasks ------

Subtask #1 (100 points): original constraints

----- Sample Input 1 ------
4
4 2 6
1 3 0 2
2 1 100
1 100
4 2 3
1 2 0 2
3 7 10
5 3 9

----- Sample Output 1 ------
NO
YES
NO
YES
----- explanation 1 ------
Example case 1:
- On the first day, the water level of the city increases to $1$ millimtre.
- On the second day, the water level increases by $3$ millimeters and becomes $1 + 3 = 4$ millimtres.
- On the third day, there is no rain in the city, so the water level decreases by $D = 2$ millimtres and becomes $4 - 2 = 2$ millimtres.
- On the fourth day, the water level increases by $2$ millimtres and becomes $2 + 2 = 4$ millimtres.

There will be no red alert in the city because the water level does not exceed $H = 6$ millimtres on any of the four days.

Example case 2: The water level of the city on the $2$-nd day is equal to $101$ millimtres, which is greater than $H = 100$ millimtres, so there will be a red alert in the city.

Example case 3: The water levels of the city on the four days are $[1, 3, 1, 3]$. The water level is equal to $H = 3$ millimtres on the second and fourth day, but it does not exceed the threshold.

Example case 4: There will be a red alert in the city on the $3$-rd day.

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