Many Easy Problems

One day, Takahashi was given the following problem from Aoki:

• You are given a tree with N vertices and an integer K. The vertices are numbered 1 through N. The edges are represented by pairs of integers (a_i, b_i).
• For a set S of vertices in the tree, let f(S) be the minimum number of the vertices in a subtree of the given tree that contains all vertices in S.
• There are ways to choose K vertices from the trees. For each of them, let S be the set of the chosen vertices, and find the sum of f(S) over all ways.
• Since the answer may be extremely large, print it modulo 924844033(prime).

Since it was too easy for him, he decided to solve this problem for all K = 1,2,...,N.

Constraints

• 2 ≦ N ≦ 200,000
• 1 ≦ a_i, b_i ≦ N
• The given graph is a tree.

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}

Output

Print N lines. The i-th line should contain the answer to the problem where K=i, modulo 924844033.

Examples

Input

3 1 2 2 3

Output

3 7 3

Input

4 1 2 1 3 1 4

Output

4 15 13 4

Input

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

Output

7 67 150 179 122 45 7

inputFormat

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}

outputFormat

Output

Print N lines. The i-th line should contain the answer to the problem where K=i, modulo 924844033.

Examples

Input

3 1 2 2 3

Output

3 7 3

Input

4 1 2 1 3 1 4

Output

4 15 13 4

Input

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

Output

7 67 150 179 122 45 7

样例

3
1 2
2 3

3
7
3

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