Phoenix and Odometers

Description:

Input:

The first line of the input contains two integers $$$n$$$ and $$$m$$$ ($$$2 \le n \le 2 \cdot 10^5$$$; $$$1 \le m \le 2 \cdot 10^5$$$) — the number of intersections and the number of roads, respectively.

Each of the next $$$m$$$ lines contain three integers $$$a_i$$$, $$$b_i$$$, and $$$l_i$$$ ($$$1 \le a_i, b_i \le n$$$; $$$a_i \neq b_i$$$; $$$1 \le l_i \le 10^9$$$) — the information about the $$$i$$$-th road. The graph is not necessarily connected. It is guaranteed that between any two intersections, there is at most one road for each direction.

The next line contains an integer $$$q$$$ ($$$1 \le q \le 2 \cdot 10^5$$$) — the number of cars.

Each of the next $$$q$$$ lines contains three integers $$$v_i$$$, $$$s_i$$$, and $$$t_i$$$ ($$$1 \le v_i \le n$$$; $$$0 \le s_i < t_i \le 10^9$$$) — the initial intersection of the $$$i$$$-th car, the initial number on the $$$i$$$-th odometer, and the number at which the $$$i$$$-th odometer resets, respectively.

Output:

Print $$$q$$$ answers. If the $$$i$$$-th car's odometer may be reset to $$$0$$$ by driving through some roads (possibly none) and returning to its starting intersection $$$v_i$$$, print YES. Otherwise, print NO.

Sample Input:

4 4
1 2 1
2 3 1
3 1 2
1 4 3
3
1 1 3
1 2 4
4 0 1

Sample Output:

YES
NO
YES

Sample Input:

4 5
1 2 1
2 3 1
3 1 2
1 4 1
4 3 2
2
1 2 4
4 3 5

Sample Output:

YES
YES

Note:

The illustration for the first example is below:

In the first query, Phoenix can drive through the following cities: $$$1$$$ $$$\rightarrow$$$ $$$2$$$ $$$\rightarrow$$$ $$$3$$$ $$$\rightarrow$$$ $$$1$$$ $$$\rightarrow$$$ $$$2$$$ $$$\rightarrow$$$ $$$3$$$ $$$\rightarrow$$$ $$$1$$$. The odometer will have reset $$$3$$$ times, but it displays $$$0$$$ at the end.

In the second query, we can show that there is no way to reset the odometer to $$$0$$$ and return to intersection $$$1$$$.

In the third query, the odometer already displays $$$0$$$, so there is no need to drive through any roads.

Below is the illustration for the second example: