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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 2010-2022 Mike Mirzayanov

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