200632: [AtCoder]ARC063 E - Integers on a Tree

Memory Limit:256 MB Time Limit:2 S
Judge Style:Text Compare Creator:
Submit:0 Solved:0

Description

Score : $800$ points

Problem Statement

We have a tree with $N$ vertices. The vertices are numbered $1, 2, ..., N$. The $i$-th ($1 ≦ i ≦ N - 1$) edge connects the two vertices $A_i$ and $B_i$.

Takahashi wrote integers into $K$ of the vertices. Specifically, for each $1 ≦ j ≦ K$, he wrote the integer $P_j$ into vertex $V_j$. The remaining vertices are left empty. After that, he got tired and fell asleep.

Then, Aoki appeared. He is trying to surprise Takahashi by writing integers into all empty vertices so that the following condition is satisfied:

  • Condition: For any two vertices directly connected by an edge, the integers written into these vertices differ by exactly $1$.

Determine if it is possible to write integers into all empty vertices so that the condition is satisfied. If the answer is positive, find one specific way to satisfy the condition.

Constraints

  • $1 ≦ N ≦ 10^5$
  • $1 ≦ K ≦ N$
  • $1 ≦ A_i, B_i ≦ N$ ($1 ≦ i ≦ N - 1$)
  • $1 ≦ V_j ≦ N$ ($1 ≦ j ≦ K$) (21:18, a mistake in this constraint was corrected)
  • $0 ≦ P_j ≦ 10^5$ ($1 ≦ j ≦ K$)
  • The given graph is a tree.
  • All $v_j$ are distinct.

Input

The input is given from Standard Input in the following format:

$N$
$A_1$ $B_1$
$A_2$ $B_2$
$:$
$A_{N-1}$ $B_{N-1}$
$K$
$V_1$ $P_1$
$V_2$ $P_2$
$:$
$V_K$ $P_K$

Output

If it is possible to write integers into all empty vertices so that the condition is satisfied, print Yes. Otherwise, print No.

If it is possible to satisfy the condition, print $N$ lines in addition. The $v$-th ($1 ≦ v ≦ N$) of these $N$ lines should contain the integer that should be written into vertex $v$. If there are multiple ways to satisfy the condition, any of those is accepted.


Sample Input 1

5
1 2
3 1
4 3
3 5
2
2 6
5 7

Sample Output 1

Yes
5
6
6
5
7

The figure below shows the tree when Takahashi fell asleep. For each vertex, the integer written beside it represents the index of the vertex, and the integer written into the vertex is the integer written by Takahashi.

6da26f89839711a520acdf5c3e1cc309.png

Aoki can, for example, satisfy the condition by writing integers into the remaining vertices as follows:

1858d5af5a2c0e51aca39a39d765debb.png

This corresponds to Sample Output 1. Note that other outputs that satisfy the condition will also be accepted, such as:

Yes
7
6
8
7
7

Sample Input 2

5
1 2
3 1
4 3
3 5
3
2 6
4 3
5 7

Sample Output 2

No

Sample Input 3

4
1 2
2 3
3 4
1
1 0

Sample Output 3

Yes
0
-1
-2
-3

The integers written by Aoki may be negative or exceed $10^6$.

Input

题意翻译

有一个$N$个点的树。顶点编号为$1$到$N$。 ███(数据已删除)为$K$个点赋上了值,其余点不定 然后,██(数据已删除)出现了。他企图通过为所有未赋值顶点赋值来震慑███(数据已删除),条件如下: * 对于任何由一条边直接连接的两个顶点,这两点点权恰好相差$1$ 确定是否有合法方案。如果有,给出一个方案

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