Tree Queries

Hanh is a famous biologist. He loves growing trees and doing experiments on his own garden.

One day, he got a tree consisting of n vertices. Vertices are numbered from 1 to n. A tree with n vertices is an undirected connected graph with n-1 edges. Initially, Hanh sets the value of every vertex to 0.

Now, Hanh performs q operations, each is either of the following types:

• Type 1: Hanh selects a vertex v and an integer d. Then he chooses some vertex r uniformly at random, lists all vertices u such that the path from r to u passes through v. Hanh then increases the value of all such vertices u by d.
• Type 2: Hanh selects a vertex v and calculates the expected value of v.

Since Hanh is good at biology but not math, he needs your help on these operations.

Input

The first line contains two integers n and q (1 ≤ n, q ≤ 150 000) — the number of vertices on Hanh's tree and the number of operations he performs.

Each of the next n - 1 lines contains two integers u and v (1 ≤ u, v ≤ n), denoting that there is an edge connecting two vertices u and v. It is guaranteed that these n - 1 edges form a tree.

Each of the last q lines describes an operation in either formats:

• 1 v d (1 ≤ v ≤ n, 0 ≤ d ≤ 10^7), representing a first-type operation.
• 2 v (1 ≤ v ≤ n), representing a second-type operation.

It is guaranteed that there is at least one query of the second type.

Output

For each operation of the second type, write the expected value on a single line.

Let M = 998244353, it can be shown that the expected value can be expressed as an irreducible fraction p/q, where p and q are integers and q not ≡ 0 \pmod{M}. Output the integer equal to p ⋅ q^{-1} mod M. In other words, output such an integer x that 0 ≤ x < M and x ⋅ q ≡ p \pmod{M}.

Example

Input

5 12 1 2 1 3 2 4 2 5 1 1 1 2 1 2 2 2 3 2 4 2 5 1 2 2 2 1 2 2 2 3 2 4 2 5

Output

1 199648871 399297742 199648871 199648871 598946614 199648873 2 2 2

Note

The image below shows the tree in the example:

For the first query, where v = 1 and d = 1:

• If r = 1, the values of all vertices get increased.
• If r = 2, the values of vertices 1 and 3 get increased.
• If r = 3, the values of vertices 1, 2, 4 and 5 get increased.
• If r = 4, the values of vertices 1 and 3 get increased.
• If r = 5, the values of vertices 1 and 3 get increased.

Hence, the expected values of all vertices after this query are (1, 0.4, 0.8, 0.4, 0.4).

For the second query, where v = 2 and d = 2:

• If r = 1, the values of vertices 2, 4 and 5 get increased.
• If r = 2, the values of all vertices get increased.
• If r = 3, the values of vertices 2, 4 and 5 get increased.
• If r = 4, the values of vertices 1, 2, 3 and 5 get increased.
• If r = 5, the values of vertices 1, 2, 3 and 4 get increased.

Hence, the expected values of all vertices after this query are (2.2, 2.4, 2, 2, 2).

inputFormat

Input

The first line contains two integers n and q (1 ≤ n, q ≤ 150 000) — the number of vertices on Hanh's tree and the number of operations he performs.

Each of the next n - 1 lines contains two integers u and v (1 ≤ u, v ≤ n), denoting that there is an edge connecting two vertices u and v. It is guaranteed that these n - 1 edges form a tree.

Each of the last q lines describes an operation in either formats:

• 1 v d (1 ≤ v ≤ n, 0 ≤ d ≤ 10^7), representing a first-type operation.
• 2 v (1 ≤ v ≤ n), representing a second-type operation.

It is guaranteed that there is at least one query of the second type.

outputFormat

Output

For each operation of the second type, write the expected value on a single line.

Let M = 998244353, it can be shown that the expected value can be expressed as an irreducible fraction p/q, where p and q are integers and q not ≡ 0 \pmod{M}. Output the integer equal to p ⋅ q^{-1} mod M. In other words, output such an integer x that 0 ≤ x < M and x ⋅ q ≡ p \pmod{M}.

Example

Input

5 12 1 2 1 3 2 4 2 5 1 1 1 2 1 2 2 2 3 2 4 2 5 1 2 2 2 1 2 2 2 3 2 4 2 5

Output

1 199648871 399297742 199648871 199648871 598946614 199648873 2 2 2

Note

The image below shows the tree in the example:

For the first query, where v = 1 and d = 1:

• If r = 1, the values of all vertices get increased.
• If r = 2, the values of vertices 1 and 3 get increased.
• If r = 3, the values of vertices 1, 2, 4 and 5 get increased.
• If r = 4, the values of vertices 1 and 3 get increased.
• If r = 5, the values of vertices 1 and 3 get increased.

Hence, the expected values of all vertices after this query are (1, 0.4, 0.8, 0.4, 0.4).

For the second query, where v = 2 and d = 2:

• If r = 1, the values of vertices 2, 4 and 5 get increased.
• If r = 2, the values of all vertices get increased.
• If r = 3, the values of vertices 2, 4 and 5 get increased.
• If r = 4, the values of vertices 1, 2, 3 and 5 get increased.
• If r = 5, the values of vertices 1, 2, 3 and 4 get increased.

Hence, the expected values of all vertices after this query are (2.2, 2.4, 2, 2, 2).

样例

5 12
1 2
1 3
2 4
2 5
1 1 1
2 1
2 2
2 3
2 4
2 5
1 2 2
2 1
2 2
2 3
2 4
2 5

1
199648871
399297742
199648871
199648871
598946614
199648873
2
2
2

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