Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

E. Little Girl and Problem on Trees

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputA 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* ≤ 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.

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

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jul/17/2019 08:42:21 (e1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|