Background

The gods toy with the mortal world. So-called fate is nothing more than a die thrown by the gods.

The butterfly that the flower cannot wait for eventually becomes a strange dream, restarting again and again.

The gods’ puppets are strangled time after time; in the name of love, they vanish into the sea of flowers of time.

Behind countless obsessions, there is always a twisted “truth”.

What you promised never appeared. Sleepless all night, perhaps I was just being self-willed, loving this human world once on your behalf.

“The most devout only pray; only the undevout have demands.”

There was never faith; by risking one’s life to save someone, one was fortunate enough to reach heaven.

Problem Description

Given an unrooted tree with $n$ nodes, each edge has a non-negative integer weight. The nodes are numbered from $1$ to $n$.

For each pair of nodes $(x, y)$, define the distance $\operatorname{dis}(x, y)$ as the XOR sum of edge weights on the unique simple path between $x$ and $y$.

Given two nodes $x, y$, define the value of node $i$ as the XOR of the distances from $x$ to $i$ and from $y$ to $i$, i.e.,

$$\operatorname{val}_{x, y}(i) = \operatorname{dis}(x, i) \oplus \operatorname{dis}(y, i) \textsf{。}$$

Now there are $q$ queries. Each query gives four integers $x, y, l, r$. You need to compute $\displaystyle \bigoplus_{i = l}^{r} \operatorname{val}_{x, y}(i)$, i.e., compute

$$\operatorname{val}_{x, y}(l) \oplus \operatorname{val}_{x, y}(l + 1) \oplus \cdots \oplus \operatorname{val}_{x, y}(r - 1) \oplus \operatorname{val}_{x, y}(r) \textsf{。}$$

In the formulas above, $\oplus$ denotes the bitwise XOR operator.

Input Format

The first line contains two integers $n, q$.

The next $n - 1$ lines each contain three integers $u, v, w$, indicating that there is an edge of weight $w$ between $u$ and $v$.

The next $q$ lines each contain four integers $x, y, l, r$, indicating one query.

Output Format

Output $q$ lines, each containing one integer, the answer to the corresponding query.

3 2
1 2 1
2 3 1
1 2 1 3
2 3 2 3

1
0

Hint

Sample Explanation

The tree given by the input is shown in the figure above. For distances between pairs of nodes, we have:

• $\operatorname{dis}(1, 1) = \operatorname{dis}(1, 3) = \operatorname{dis}(2, 2) = \operatorname{dis}(3, 1) = \operatorname{dis}(3, 3) = 0$, and
• $\operatorname{dis}(1, 2) = \operatorname{dis}(2, 1) = \operatorname{dis}(2, 3) = \operatorname{dis}(3, 2) = 1$.

Query $1$: $\operatorname{val}_{1, 2}(1) \oplus \operatorname{val}_{1, 2}(2) \oplus \operatorname{val}_{1, 2}(3) = (0 \oplus 1) \oplus (1 \oplus 0) \oplus (0 \oplus 1) = 1 \oplus 1 \oplus 1 = 1$.

Query $2$: $\operatorname{val}_{2, 3}(2) \oplus \operatorname{val}_{2, 3}(3) = (0 \oplus 1) \oplus (1 \oplus 0) = 1 \oplus 1 = 0$.

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Constraints

This problem uses bundled testdata.

Subtask ID	$n \le$	$q \le$	Score
1	$100$	$10$	24
2	$10^6$		14
3	$100$	$10^6$
4	$10^6$		48

For $100\%$ of the data, it is guaranteed that $1 \le n, q \le {10}^6$, $1 \le u, v, x, y \le n$, $1 \le l \le r \le n$, and $0 \le w < 2^{31}$.

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Hint

The maximum I/O size of this problem reaches 60 MiB. Please pay attention to I/O efficiency.

Translated by ChatGPT 5