Hongjun and the Tree

You are given a tree with $N$ vertices rooted at vertex 1. Every vertex starts with weight 0.

Process $Q$ queries in the given order. There are two kinds.

• Type 1, written as 1 v x k: add $x$ to the weight of vertex $v$, and add $x - i \times k$ to the weight of every vertex that lies in the subtree of $v$ at distance $i$ from $v$. ($1 \le v \le N$, $0 \le x, k < 10^9+7$)
• Type 2, written as 2 v: print the current weight of vertex $v$ modulo $10^9+7$. ($1 \le v \le N$)

A weight can become negative. The answer to a type 2 query is always a residue between 0 and $10^9+6$.

The first line contains the number of vertices $N$ and the number of queries $Q$. ($1 \le N \le 300\,000$, $1 \le Q \le 300\,000$)

The second line contains $N-1$ integers $p_2, p_3, \dots, p_N$. Here $p_k$ is the parent of vertex $k$ and satisfies $1 \le p_k < k$. When $N$ is 1, the second line is empty.

Each of the next $Q$ lines contains one query. The first integer on a line is the query type, followed by the integers that type takes.

For each type 2 query, print its answer on its own line, in input order.