We have a tree consisting of $N$ vertices numbered from $0$ to $N-1$. Additionally, an integer sequence $A_0, A_1, \ldots, A_{N-1}$ of length $N$ is given.

For integers $l, r$ satisfying $0 \le l < r \le N$, vertices $v, d$, and a nonnegative integer $k$, define $f(l, r, v, d, k) = 10^{-999999999} dist(v, d) + \sum_{i = l}^{r - 1} (A_i + k) dist(v, i)$. Here, $dist(a, b)$ is the length of the shortest path between two vertices $a$ and $b$.

The following queries must be processed:

• l r d k: Output the vertex $v$ that minimizes $f(l, r, v, d, k)$. It can be proven that such $v$ is unique.

Note that the queries are given online. See the Input section for details.

Input

The first line contains the size of the tree $N$. ($1 \le N \le 150{,}000$)

The next $N-1$ lines each contain two integers $u, v$, indicating that there is an edge connecting vertices $u$ and $v$. ($0 \le u, v \le N-1$)

The next line contains the sequence $A_0, A_1, \ldots, A_{N-1}$. ($0 \le A_i \le 150{,}000$)

The next line contains the number of queries $Q$. ($1 \le Q \le 150{,}000$)

The next $Q$ lines each contain four integers $a, b, z, d$. ($0 \le a, b, d \le N-1$, $0 \le z \le 150{,}000$)

Let $X_i$ be the answer to the $i$-th query ($0 \le i \le Q-1$). For the $i$-th query, $l, r, k$ can be recovered by the following formulas. $d$ is used as given in the input.

• $a^\prime = (a + \sum_{j = 0}^{i - 1} X_j) \bmod N$
• $b^\prime = (b + 2 \sum_{j = 0}^{i - 1} X_j) \bmod N$
• $k = (z + (\sum_{j = 0}^{i - 1} X_j)^2) \bmod 150\,001$
• $l = \min(a^\prime, b^\prime)$
• $r = 1 + \max(a^\prime, b^\prime)$

Output

Output the answers to the problem over $Q$ lines, one per line.

Examples

Input 1

5
0 1
1 3
3 2
3 4
1000 10 1 100 10000
15
0 0 0 0
0 1 150000 1
2 0 0 2
3 0 150000 3
4 2 150000 4
1 1 149975 0
0 0 149965 1
1 2 149951 2
1 4 149901 3
3 4 149804 4
2 0 149745 0
3 1 149639 1
1 4 149517 2
4 3 149375 3
0 1 149160 4

Output 1

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