Problem3322--Little Girl and Problem on Trees

3322: Little Girl and Problem on Trees

Time Limit: 2 Sec  Memory Limit: 256 MB
Submit: 0  Solved: 0
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Description

time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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.
Input

The first line contains integers n (2≤n≤105) and q (1≤q≤105) − the number of tree nodes and the number of requests, correspondingly.

Each of the next n-1 lines contains two integers ui and vi (1≤ui,vi≤n, ui≠vi), that show that there is an edge between nodes ui and vi. 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≤104, 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.

Output

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

Examples
Input
3 6
1 2
1 3
0 3 1 2
0 2 3 1
0 1 5 2
1 1
1 2
1 3
Output
9
9
6
Input
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
Output
11
17
11
16
17
11

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