Appleman has a tree with n vertices. Some of the vertices (at least one) are colored black and other vertices are colored white.

Consider a set consisting of k (0 ≤ k < n) edges of Appleman's tree. If Appleman deletes these edges from the tree, then it will split into (k + 1) parts. Note, that each part will be a tree with colored vertices.

Now Appleman wonders, what is the number of sets splitting the tree in such a way that each resulting part will have exactly one black vertex? Find this number modulo 1000000007 (10^9 + 7).


-----Input-----

The first line contains an integer n (2  ≤ n ≤ 10^5) — the number of tree vertices. 

The second line contains the description of the tree: n - 1 integers p_0, p_1, ..., p_{n} - 2 (0 ≤ p_{i} ≤ i). Where p_{i} means that there is an edge connecting vertex (i + 1) of the tree and vertex p_{i}. Consider tree vertices are numbered from 0 to n - 1.

The third line contains the description of the colors of the vertices: n integers x_0, x_1, ..., x_{n} - 1 (x_{i} is either 0 or 1). If x_{i} is equal to 1, vertex i is colored black. Otherwise, vertex i is colored white.


-----Output-----

Output a single integer — the number of ways to split the tree modulo 1000000007 (10^9 + 7).


-----Examples-----
Input
3
0 0
0 1 1

Output
2

Input
6
0 1 1 0 4
1 1 0 0 1 0

Output
1

Input
10
0 1 2 1 4 4 4 0 8
0 0 0 1 0 1 1 0 0 1

Output
27

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'MOD = 1000000007\n\nn = int(input())\np = [int(x) for x in input().split()]\nx = [int(x) for x in input().split()]\n\nchildren = [[] for x in range(n)]\n\nfor i in range(1,n):\n    children[p[i-1]].append(i)\n\n#print(children)\n\ncount = [(0,0) for i in range(n)]\nfor i in reversed(list(range(n))):\n    prod = 1\n    for ch in children[i]:\n        prod *= count[ch][0]+count[ch][1]\n    if x[i]:\n        count[i] = (0,prod % MOD)\n    else:\n        tot = 0\n        for ch in children[i]:\n            cur = count[ch][1]*prod // (count[ch][0]+count[ch][1])\n            tot += cur\n        count[i] = (prod % MOD, tot % MOD)\n\nprint(count[0][1])\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13505