Problem2922--On Changing Tree

2922: On Changing Tree

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

You are given a rooted tree consisting of n vertices numbered from 1 to n. The root of the tree is a vertex number 1.

Initially all vertices contain number 0. Then come q queries, each query has one of the two types:

  • The format of the query: 1 v x k. In response to the query, you need to add to the number at vertex v number x; to the numbers at the descendants of vertex v at distance 1, add x-k; and so on, to the numbers written in the descendants of vertex v at distance i, you need to add x-(i·k). The distance between two vertices is the number of edges in the shortest path between these vertices.
  • The format of the query: 2 v. In reply to the query you should print the number written in vertex v modulo 1000000007 (109+7).

Process the queries given in the input.

Input

The first line contains integer n (1≤n≤3·105) −the number of vertices in the tree. The second line contains n-1 integers p2,p3,... pn (1≤pi<i), where pi is the number of the vertex that is the parent of vertex i in the tree.

The third line contains integer q (1≤q≤3·105) − the number of queries. Next q lines contain the queries, one per line. The first number in the line is type. It represents the type of the query. If type=1, then next follow space-separated integers v,x,k (1≤v≤n; 0≤x<109+7; 0≤k<109+7). If type=2, then next follows integer v (1≤v≤n) −the vertex where you need to find the value of the number.

Output

For each query of the second type print on a single line the number written in the vertex from the query. Print the number modulo 1000000007 (109+7).

Examples
Input
3
1 1
3
1 1 2 1
2 1
2 2
Output
2
1
Note

You can read about a rooted tree here: http://en.wikipedia.org/wiki/Tree_(graph_theory).

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