Once there was a courier named Kujou Kawaii, whose work was to collect packages from people around the city. The city consisted of $n$ communities, numbered from $1$ to $n$, together with $n -1$ bidirectional roads connecting them. The express distribution center of this city was located at the community numbered $k$. Of course, any two communities were guaranteed to be connected by these roads. Kujou's electromobile was so small that she could only carry packages from $1$ community at the same time. She would always first deliver packages from the community numbered $1$, then those from the one numbered $2$, etc., and finally the packages from the one numbered $n$.
Let's calculate Kujou's tiredness index after a whole day of work! We only consider the trip from each community to the express distribution center. Unfortunately, Kujou had no sense of direction. On arriving at a community, she would uniformly randomly choose a road (including the one she came from) to follow, until she finally reached the community where the express distribution center was located. Suppose the trip from the community numbered $i$ to the express center passed $d_i$ roads. Kujou's tiredness was influenced by three factors.
It can be shown that $m_i$ can be expressed as an irreducible fraction $frac(p_i, q_i)$, where $p_i$ and $q_i$ are integers. It is then guaranteed in all test cases that $q_i not equiv 0 pmod 10^9 + 7$. In this case, $m_i$ modulo $10^9 + 7$ is well-defined, which is some integer $m '_i$ such that $m '_i q_i equiv p_i pmod 10^9 + 7$. Furthermore, you only need to output $m '_1 plus.circle \\dots plus.circle m '_n$ to prevent large output, where $plus.circle$ denotes the bitwise XOR operation.
The first line contains four integers $n$, $k$, $p_x$ and $q_x$ ($2 <= n <= 10^5, 1 <= k <= n, 1 <= p_x <= q_x <= 10^7$), where $x$ is given in the form $p_x \/ q_x$.
Each of the next $n -1$ lines contains two integers $u$ and $v$ ($1 <= u, v <= n$), indicating that there was a road connecting the community numbered $u$ and the one numbered $v$. It is guaranteed that all communities are connected by these $n -1$ roads.
Print $m '_1 plus.circle \\dots plus.circle m '_n$.
In the second example, $m_1 = 0$, $m_2 = frac(36, 49)$, $m_3 = frac(48, 49)$.
## Input
The first line contains four integers $n$, $k$, $p_x$ and $q_x$ ($2 <= n <= 10^5, 1 <= k <= n, 1 <= p_x <= q_x <= 10^7$), where $x$ is given in the form $p_x \/ q_x$.Each of the next $n -1$ lines contains two integers $u$ and $v$ ($1 <= u, v <= n$), indicating that there was a road connecting the community numbered $u$ and the one numbered $v$. It is guaranteed that all communities are connected by these $n -1$ roads.
## Output
Print $m '_1 plus.circle \\dots plus.circle m '_n$.
[samples]
## Note
In the second example, $m_1 = 0$, $m_2 = frac(36, 49)$, $m_3 = frac(48, 49)$.
**Definitions**
Let $ n \in \mathbb{Z} $ be the number of communities, $ k \in \{1, \dots, n\} $ the location of the express center.
Let $ G = (V, E) $ be a tree with $ V = \{1, \dots, n\} $, $ |E| = n-1 $, and edge set $ E $.
Let $ d_i $ be the graph distance (number of edges) from node $ i $ to node $ k $.
Let $ x = \frac{p_x}{q_x} \in (0,1) $ be a given rational probability.
For each community $ i \in \{1, \dots, n\} $, define $ m_i $ as the expected number of steps for a random walk starting at $ i $, where at each node the walker chooses uniformly at random among all incident edges (including the one just traversed), until reaching $ k $.
Let $ m_i = \frac{p_i}{q_i} $ in lowest terms. Define $ m'_i \in \mathbb{Z}/(10^9+7)\mathbb{Z} $ such that $ m'_i \cdot q_i \equiv p_i \pmod{10^9+7} $.
**Constraints**
1. $ 2 \leq n \leq 10^5 $
2. $ 1 \leq k \leq n $
3. $ 1 \leq p_x < q_x \leq 10^7 $
4. The graph is a tree.
5. $ q_i \not\equiv 0 \pmod{10^9+7} $ for all $ i $.
**Objective**
Compute $ \bigoplus_{i=1}^n m'_i $, where $ \oplus $ denotes bitwise XOR.