E. Little Girl and Problem on Trees

хугацааны хязгаарлалт 2 секунд

санах ойн хязгаарлалт 256 мегабайт

оролт стандарт оролт

гаралт стандарт гаралт

A little girl loves problems on trees very much. Here's one of them.

A tree is an undirected connected graph, not containing cycles. The degree of node $x$ in the tree is the number of nodes $y$ of the tree, such that each of them is connected with node $x$ by some edge of the tree.

Let's consider a tree that consists of $n$ nodes. We'll consider the tree's nodes indexed from 1 to $n$. The cosidered tree has the following property: each node except for node number 1 has the degree of at most 2.

Initially, each node of the tree contains number 0. Your task is to quickly process the requests of two types:

  • Request of form: $0$ $v$ $x$ $d$. In reply to the request you should add $x$ to all numbers that are written in the nodes that are located at the distance of at most $d$ from node $v$. The distance between two nodes is the number of edges on the shortest path between them.
  • Request of form: $1$ $v$. In reply to the request you should print the current number that is written in node $v$.

Оролт

The first line contains integers $n$ ($2 ≤ n ≤ 10^{5}$) and $q$ ($1 ≤ q ≤ 10^{5}$) -- the number of tree nodes and the number of requests, correspondingly.

Each of the next $n  -  1$ lines contains two integers $u_{i}$ and $v_{i}$ ($1 ≤ u_{i}, v_{i} ≤ n$, $u_{i} ≠ v_{i}$), that show that there is an edge between nodes $u_{i}$ and $v_{i}$. Each edge's description occurs in the input exactly once. It is guaranteed that the given graph is a tree that has the property that is described in the statement.

Next $q$ lines describe the requests.

  • The request to add has the following format: $0$ $v$ $x$ $d$ ($1 ≤ v ≤ n$, $1 ≤ x ≤ 10^{4}$, $1 ≤ d < n$).
  • The request to print the node value has the following format: $1$ $v$ ($1 ≤ v ≤ n$).

The numbers in the lines are separated by single spaces.

Гаралт

For each request to print the node value print an integer -- the reply to the request.

Орчуулсан: [орчуулагдаж байгаа]

Жишээ тэстүүд

Оролт
3 6
1 2
1 3
0 3 1 2
0 2 3 1
0 1 5 2
1 1
1 2
1 3
Гаралт
9
9
6
Оролт
6 11
1 2
2 5
5 4
1 6
1 3
0 3 1 3
0 3 4 5
0 2 1 4
0 1 5 5
0 4 6 2
1 1
1 2
1 3
1 4
1 5
1 6
Гаралт
11
17
11
16
17
11
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