Little John is as little as night is day — he was known to be a giant, at possibly $$$2.1$$$ metres tall. It has everything to do with his love for milk.

His dairy diary has $$$n$$$ entries, showing that he acquired $$$a_i$$$ pints of fresh milk on day $$$d_i$$$. Milk declines in freshness with time and stays drinkable for a maximum of $$$k$$$ days. In other words, fresh milk acquired on day $$$d_i$$$ will be drinkable between days $$$d_i$$$ and $$$d_i+k-1$$$ inclusive.

Every day, Little John drinks drinkable milk, up to a maximum of $$$m$$$ pints. In other words, if there are less than $$$m$$$ pints of milk, he will drink them all and not be satisfied; if there are at least $$$m$$$ pints of milk, he will drink exactly $$$m$$$ pints and be satisfied, and it's a milk satisfaction day.

Little John always drinks the freshest drinkable milk first.

Determine the number of milk satisfaction days for Little John.

Input format:
The first line of the input contains a single integer $$$t$$$ ($$$1\leq t \leq 10^4$$$), the number of test cases.

The first line of each test case consists of three integers $$$n$$$, $$$m$$$, $$$k$$$ ($$$1\le n$$$, $$$m$$$, $$$k \le 10^5$$$), the number of diary entries, the maximum pints needed for a milk satisfaction day, and the duration of milk's freshness.

Then follow $$$n$$$ lines of each test case, each with two integers $$$d_i$$$ and $$$a_i$$$ ($$$1\le d_i$$$, $$$a_i \le 10^6$$$), the day on which the milk was acquired and the number of pints acquired. They are sorted in increasing values of $$$d_i$$$, and all values of $$$d_i$$$ are distinct.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.
Output format:
For each test case, output a single integer, the number of milk satisfaction days.
Example Input 0:
6
1 1 3
1 5
2 3 3
1 5
2 7
4 5 2
1 9
2 6
4 9
5 6
5 2 4
4 7
5 3
7 1
11 2
12 1
4 1 3
5 10
9 4
14 8
15 3
5 5 5
8 9
10 7
16 10
21 5
28 9

Example Output 0:
3
3
4
5
10
6

Notes:
In the first test case, $$$5$$$ pints of milk are good for $$$3$$$ days before spoiling.

In the second test case, the following will happen:

- On day $$$1$$$, he will receive $$$5$$$ pints of milk and drink $$$3$$$ of them (leaving $$$2$$$ pints from day $$$1$$$);
- On day $$$2$$$, he will receive $$$7$$$ pints of milk and drink $$$3$$$ of them (leaving $$$2$$$ pints from day $$$1$$$ and $$$4$$$ pints from day $$$2$$$);
- On day $$$3$$$, he will drink $$$3$$$ pints from day $$$2$$$ (leaving $$$2$$$ pints from day $$$1$$$ and $$$1$$$ pint from day $$$2$$$);
- On day $$$4$$$, the milk acquired on day $$$1$$$ will spoil, and he will drink $$$1$$$ pint from day $$$2$$$ (no more milk is left).

Example input:
6
1 1 3
1 5
2 3 3
1 5
2 7
4 5 2
1 9
2 6
4 9
5 6
5 2 4
4 7
5 3
7 1
11 2
12 1
4 1 3
5 10
9 4
14 8
15 3
5 5 5
8 9
10 7
16 10
21 5
28 9


Example output:
3
3
4
5
10
6