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 (10<sup class="upper-index">9</sup> + 7). 
Process the queries given in the input.
The first line contains integer *n* (1 ≤ *n* ≤ 3·10<sup class="upper-index">5</sup>) — the number of vertices in the tree. The second line contains *n* - 1 integers *p*<sub class="lower-index">2</sub>, *p*<sub class="lower-index">3</sub>, ... *p*<sub class="lower-index">*n*</sub> (1 ≤ *p*<sub class="lower-index">*i*</sub> &lt; *i*), where *p*<sub class="lower-index">*i*</sub> is the number of the vertex that is the parent of vertex *i* in the tree.

The third line contains integer *q* (1 ≤ *q* ≤ 3·10<sup class="upper-index">5</sup>) — 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* &lt; 10<sup class="upper-index">9</sup> + 7; 0 ≤ *k* &lt; 10<sup class="upper-index">9</sup> + 7). If *type* = 2, then next follows integer *v* (1 ≤ *v* ≤ *n*) — the vertex where you need to find the value of the number.
def getdistance(orvertice,dstvertice):
    distance=0
    actual=orvertice
    while not actual is dstvertice:
        if actual['P']==-1:
            raise ValueError('Not a descendent')
        actual=actual['P']
        distance+=1
    return distance
vertices=list()
input()
vertices.append({'P':-1,'V':0})
for parent in input().split(' '):
    vertices.append({'P':vertices[int(parent)-1],'V':0})
for i in range(0,int(input())):
    query = input().split(' ')
    if int(query[0]) == 1:
        for vertice in vertices:
            try:
                vertice['V'] += int(query[2]) - int(query[3]) * getdistance(vertice,vertices[int(query[1])-1])
            except Exception as e:
                pass
    else:
        print(vertices[int(query[1])-1]['V']%1000000007)