#include <bits/stdc++.h>
using namespace std;
long long xrange[4 * 300000 + 5];
long long krange[4 * 300000 + 5];
int depth[300000];
std::vector<int> children[300000];
int indexInRangeTree[300000 + 5], startRange[300000 + 5], endRange[300000 + 5];
int totId;
void compute_tree_ranges(int c, int h) {
  depth[c] = h;
  indexInRangeTree[c] = startRange[c] = totId++;
  for (int nxt : children[c]) {
    compute_tree_ranges(nxt, h + 1);
  }
  endRange[c] = totId;
}
void update(int uL, int uR, long long x, long long k, int v, int i = 1,
            int cLeft = 0, int cRight = 300000) {
  if (uL == cLeft && uR == cRight) {
    xrange[i] = (xrange[i] + x + ((depth[v] * k) % 1000000007)) % 1000000007;
    krange[i] = (krange[i] + k) % 1000000007;
    return;
  }
  int mid = (cLeft + cRight) / 2;
  if (uL < mid) update(uL, min(uR, mid), x, k, v, i * 2, cLeft, mid);
  if (uR > mid) update(max(uL, mid), uR, x, k, v, i * 2 + 1, mid, cRight);
}
long long query(int uL, int uR, int v, int acc_k = 0, int i = 1, int cLeft = 0,
                int cRight = 300000) {
  if (uL == cLeft && uR == cRight) {
    return ((xrange[i] % 1000000007) -
            (((depth[v] % 1000000007) *
              ((acc_k % 1000000007) + (krange[i] % 1000000007)) % 1000000007) %
             1000000007)) %
           1000000007;
  }
  int mid = (cLeft + cRight) / 2;
  long long ans = xrange[i];
  if (indexInRangeTree[v] < mid)
    ans = (ans + query(uL, min(uR, mid), v, (acc_k + krange[i]) % 1000000007,
                       i * 2, cLeft, mid) %
                     1000000007) %
          1000000007;
  else
    ans = (ans + query(max(uL, mid), uR, v, (acc_k + krange[i]) % 1000000007,
                       i * 2 + 1, mid, cRight) %
                     1000000007) %
          1000000007;
  return ans;
}
void update_node(int id, int x, int k) {
  update(startRange[id], endRange[id], x, k, id);
}
long long query_subtree(int id) {
  auto res = query(startRange[id], endRange[id], id);
  if (res < 0) {
    return 1000000007 + res;
  }
  return res;
}
int main(void) {
  std::ios::sync_with_stdio(false);
  int n, q, code, v, x, k;
  std::cin >> n;
  for (int i = 1; i < n; i++) {
    std::cin >> x;
    children[x - 1].push_back(i);
  }
  compute_tree_ranges(0, 0);
  std::cin >> q;
  for (int i = 0; i < q; i++) {
    std::cin >> code;
    if (code == 1) {
      std::cin >> v >> x >> k;
      update_node(v - 1, x, k);
    } else {
      std::cin >> v;
      std::cout << query_subtree(v - 1) << std::endl;
    }
  }
}

### Prompt

Your task is to create a Cpp solution to the following problem:

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).

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
long long xrange[4 * 300000 + 5];
long long krange[4 * 300000 + 5];
int depth[300000];
std::vector<int> children[300000];
int indexInRangeTree[300000 + 5], startRange[300000 + 5], endRange[300000 + 5];
int totId;
void compute_tree_ranges(int c, int h) {
  depth[c] = h;
  indexInRangeTree[c] = startRange[c] = totId++;
  for (int nxt : children[c]) {
    compute_tree_ranges(nxt, h + 1);
  }
  endRange[c] = totId;
}
void update(int uL, int uR, long long x, long long k, int v, int i = 1,
            int cLeft = 0, int cRight = 300000) {
  if (uL == cLeft && uR == cRight) {
    xrange[i] = (xrange[i] + x + ((depth[v] * k) % 1000000007)) % 1000000007;
    krange[i] = (krange[i] + k) % 1000000007;
    return;
  }
  int mid = (cLeft + cRight) / 2;
  if (uL < mid) update(uL, min(uR, mid), x, k, v, i * 2, cLeft, mid);
  if (uR > mid) update(max(uL, mid), uR, x, k, v, i * 2 + 1, mid, cRight);
}
long long query(int uL, int uR, int v, int acc_k = 0, int i = 1, int cLeft = 0,
                int cRight = 300000) {
  if (uL == cLeft && uR == cRight) {
    return ((xrange[i] % 1000000007) -
            (((depth[v] % 1000000007) *
              ((acc_k % 1000000007) + (krange[i] % 1000000007)) % 1000000007) %
             1000000007)) %
           1000000007;
  }
  int mid = (cLeft + cRight) / 2;
  long long ans = xrange[i];
  if (indexInRangeTree[v] < mid)
    ans = (ans + query(uL, min(uR, mid), v, (acc_k + krange[i]) % 1000000007,
                       i * 2, cLeft, mid) %
                     1000000007) %
          1000000007;
  else
    ans = (ans + query(max(uL, mid), uR, v, (acc_k + krange[i]) % 1000000007,
                       i * 2 + 1, mid, cRight) %
                     1000000007) %
          1000000007;
  return ans;
}
void update_node(int id, int x, int k) {
  update(startRange[id], endRange[id], x, k, id);
}
long long query_subtree(int id) {
  auto res = query(startRange[id], endRange[id], id);
  if (res < 0) {
    return 1000000007 + res;
  }
  return res;
}
int main(void) {
  std::ios::sync_with_stdio(false);
  int n, q, code, v, x, k;
  std::cin >> n;
  for (int i = 1; i < n; i++) {
    std::cin >> x;
    children[x - 1].push_back(i);
  }
  compute_tree_ranges(0, 0);
  std::cin >> q;
  for (int i = 0; i < q; i++) {
    std::cin >> code;
    if (code == 1) {
      std::cin >> v >> x >> k;
      update_node(v - 1, x, k);
    } else {
      std::cin >> v;
      std::cout << query_subtree(v - 1) << std::endl;
    }
  }
}

```