Codeforces 461 B. Appleman and Tree

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 (109?+?7).

Input

The first line contains an integer n (2??≤?n?≤?105) — the number of tree vertices.

The second line contains the description of the tree: n?-?1 integers p0,?p1,?...,?pn?-?2 (0?≤?pi?≤?i). Where pi means that there is an edge connecting vertex (i?+?1) of the tree and vertex pi. Consider tree vertices are numbered from 0 to n?-?1.

The third line contains the description of the colors of the vertices: n integers x0,?x1,?...,?xn?-?1 (xi is either 0 or 1). If xi is equal to1, 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 (109?+?7).

Sample test(s)

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

#include <iostream> #include <cstdio> #include <cstring> #include <algorithm> using namespace std; const int maxn=100010; const long long int mod=1000000007LL; int n; struct Edge { int to,next; }edge[3*maxn]; int Adj[maxn],Size; void init() { Size=0; memset(Adj,-1,sizeof(Adj)); } void Add_Edge(int u,int v) { edge[Size].to=v; edge[Size].next=Adj[u]; Adj[u]=Size++; } int c[maxn]; long long int dp[maxn][2]; void dfs(int u,int fa) { dp[u][c[u]]=1; for(int i=Adj[u];~i;i=edge[i].next) { int v=edge[i].to; if(v==fa) continue; dfs(v,u); dp[u][1]=(dp[u][1]*dp[v][1]%mod+dp[u][0]*dp[v][1]%mod+dp[u][1]*dp[v][0]%mod)%mod; dp[u][0]=(dp[u][0]*dp[v][0]%mod+dp[u][0]*dp[v][1]%mod)%mod; } } int main() { init(); scanf("%d",&n); for(int i=1;i<n;i++) { int v; scanf("%d",&v); Add_Edge(i,v); Add_Edge(v,i); } for(int i=0;i<n;i++) scanf("%d",c+i); dfs(0,0); printf("%I64d\n",dp[0][1]); return 0; }