CF1760G.SlavicG's Favorite Problem

You are given a weighted tree with $n$ vertices. Recall that a tree is a connected graph without any cycles. A weighted tree is a tree in which each edge has a certain weight. The tree is undirected, it doesn't have a root.

Since trees bore you, you decided to challenge yourself and play a game on the given tree.

In a move, you can travel from a node to one of its neighbors (another node it has a direct edge with).

You start with a variable $x$ which is initially equal to $0$. When you pass through edge $i$, $x$ changes its value to $x ~\mathsf{XOR}~ w_i$ (where $w_i$ is the weight of the $i$-th edge).

Your task is to go from vertex $a$ to vertex $b$, but you are allowed to enter node $b$ if and only if after traveling to it, the value of $x$ will become $0$. In other words, you can travel to node $b$ only by using an edge $i$ such that $x ~\mathsf{XOR}~ w_i = 0$. Once you enter node $b$ the game ends and you win.

Additionally, you can teleport at most once at any point in time to any vertex except vertex $b$. You can teleport from any vertex, even from $a$.

Answer with "YES" if you can reach vertex $b$ from $a$, and "NO" otherwise.

Note that $\mathsf{XOR}$ represents the bitwise XOR operation.

你被给定一棵包含 $n$ 个顶点的带权树。回忆一下，树是一种无环的连通图。带权树是指每条边都具有某个权重的树。该树是无向的，没有根节点。

由于树让你感到乏味，你决定挑战自我，在给定的树上进行一场游戏。

在一次移动中，你可以从一个节点移动到其任意一个相邻节点（即与之有直接边相连的另一节点）。

你初始时拥有一个变量 $x$，其值为 $0$。当你经过第 $i$ 条边时，$x$ 的值会更新为 $x ~\mathsf{XOR}~ w_i$（其中 $w_i$ 表示第 $i$ 条边的权重）。

你的任务是从顶点 $a$ 出发到达顶点 $b$，但你仅当抵达 $b$ 后 $x$ 的值恰好变为 $0$ 时，才被允许进入节点 $b$。换言之，你只能通过某条边 $i$ 进入 $b$，且必须满足 $x ~\mathsf{XOR}~ w_i = 0$。一旦你进入节点 $b$，游戏立即结束，你获胜。

此外，你最多可使用一次瞬移：在任意时刻，你可以瞬移到除顶点 $b$ 外的任意顶点（包括从 $a$ 或任意其他顶点瞬移）。

若能从顶点 $a$ 到达顶点 $b$，输出 "YES"；否则输出 "NO"。

注意：$\mathsf{XOR}$ 表示按位异或运算。

The first line contains a single integer $t$ ($1 \leq t \leq 1000$) — the number of test cases.

The first line of each test case contains three integers $n$, $a$, and $b$ ($2 \leq n \leq 10^5$), ($1 \leq a, b \leq n; a \ne b$) — the number of vertices, and the starting and desired ending node respectively.

Each of the next $n-1$ lines denotes an edge of the tree. Edge $i$ is denoted by three integers $u_i$, $v_i$ and $w_i$ — the labels of vertices it connects ($1 \leq u_i, v_i \leq n; u_i \ne v_i; 1 \leq w_i \leq 10^9$) and the weight of the respective edge.

It is guaranteed that the sum of $n$ over all test cases does not exceed $10^5$.

第一行包含一个整数 $t$（$1 \leq t \leq 1000$）——测试用例的数量。

每个测试用例的第一行包含三个整数 $n$、$a$ 和 $b$（$2 \leq n \leq 10^5$，$1 \leq a, b \leq n$；且 $a \ne b$）——分别表示顶点数量、起点和目标终点。

接下来的 $n-1$ 行每行描述树中的一条边。第 $i$ 条边由三个整数 $u_i$、$v_i$ 和 $w_i$ 表示——即该边所连接的两个顶点的编号（$1 \leq u_i, v_i \leq n$；$u_i \ne v_i$；$1 \leq w_i \leq 10^9$）以及该边的权重。

保证所有测试用例中 $n$ 的总和不超过 $10^5$。

For each test case output "YES" if you can reach vertex $b$, and "NO" otherwise.

对于每个测试用例，若可以到达顶点 $b$，则输出 “YES”，否则输出 “NO”。

For the first test case, we can travel from node $1$ to node $3$, $x$ changing from $0$ to $1$, then we travel from node $3$ to node $2$, $x$ becoming equal to $3$. Now, we can teleport to node $3$ and travel from node $3$ to node $4$, reaching node $b$, since $x$ became equal to $0$ in the end, so we should answer "YES".

For the second test case, we have no moves, since we can't teleport to node $b$ and the only move we have is to travel to node $2$ which is impossible since $x$ wouldn't be equal to $0$ when reaching it, so we should answer "NO".

对于第一个测试用例，我们可以从节点 $1$ 走到节点 $3$，此时 $x$ 从 $0$ 变为 $1$；接着从节点 $3$ 走到节点 $2$，此时 $x$ 变为 $3$。此时，我们可以传送到节点 $3$，再从节点 $3$ 走到节点 $4$（即目标节点 $b$），最终 $x$ 恰好变为 $0$，因此应输出 "YES"。

对于第二个测试用例，我们无法进行任何操作：既不能直接传送到节点 $b$，唯一可行的移动是走到节点 $2$，但该操作不可行，因为到达节点 $2$ 时 $x$ 不会等于 $0$。因此应输出 "NO"。