On Changing Tree

2000ms

262144K

Description:

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, ... p_n (1 ≤ p_i < i), where p_i 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).

Sample Input:

Sample Output:

2
1

Note:

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

Informação

Provedor Codeforces

Código CF396C