HDU5739 Fantasia【点双连通分量 割点】

//#pragma GCC optimize("O3")
//#pragma comment(linker, "/STACK:1024000000,1024000000")
#include<bits/stdc++.h>
using namespace std;
function<void(void)> ____ = [](){ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);};
typedef long long int LL;
const int MAXN = 2e5+7;
const LL MOD = 1e9+7;
int n,m,bccid[MAXN],dfn[MAXN],low[MAXN],ID,w[MAXN],bel[MAXN],idx;
vector<int> G[MAXN],pt[MAXN];
LL tot,ans,f[MAXN],gw[MAXN],mul[MAXN],subsum[MAXN],submul[MAXN];
bool iscut[MAXN];
LL ksm(LL a, LL b){
    LL ret = 1;
    while(b){
        if(b&1) ret = ret * a % MOD;
        b >>= 1;
        a = a * a % MOD;
    }
    return ret;
}
LL inv(LL x){ return ksm(x,MOD-2); }
void init(){
    for(int i = 1; i <= n; i++) G[i].clear();
    memset(dfn+1,0,n<<2);
    memset(bel+1,0,n<<2);
    memset(iscut+1,0,n);
    fill(submul+1,submul+1+n,1);
    fill(subsum+1,subsum+1+n,0);
    ans = tot = ID = idx = 0;
}
void tarjan(int u, int par, int id){
    pt[id].push_back(u);
    bel[u] = id;
    dfn[u] = low[u] = ++idx;
    mul[id] = mul[id] * w[u] % MOD;
    int child = 0;
    for(int v : G[u]){
        if(v==par) continue;
        if(!dfn[v]){
            child++;
            LL tmp = mul[ID];
            tarjan(v,u,id);
            low[u] = min(low[u],low[v]);
            if(low[v]>=dfn[u]){
                if(par) iscut[u] = true;
                LL sub = mul[ID] * inv(tmp) % MOD;
                // 由于不确定根节点是否是割点，所以先当作割点来处理
                subsum[u] = (subsum[u] + sub) % MOD;
                submul[u] = submul[u] * sub % MOD;
            }
        }
        else low[u] = min(low[u],dfn[v]);
    }
    if(!par and child > 1) iscut[u] = true;
}
void solve(){
    scanf("%d %d",&n,&m);
    init();
    for(int i = 1; i <= n; i++) scanf("%d",&w[i]);
    for(int i = 1; i <= m; i++){
        int u, v; scanf("%d %d",&u,&v);
        G[u].push_back(v); G[v].push_back(u);
    }
    for(int i = 1; i <= n; i++) if(!dfn[i]){
        pt[++ID].clear();
        mul[ID] = 1;
        tarjan(i,0,ID);
        tot = (tot + mul[ID]) % MOD;
        for(int x : pt[ID]){
            if(x==i) continue;
            subsum[x] = (subsum[x] + mul[ID] * inv(submul[x]*w[x]%MOD) % MOD) % MOD;
        }
    }
    for(int i = 1; i <= n; i++){
        LL res = 0;
        if(iscut[i]) res = (tot - mul[bel[i]] + subsum[i] + MOD) % MOD;
        else{
            if(pt[bel[i]].size() == 1) res = (tot - w[i] + MOD) % MOD;
            else res = (tot - mul[bel[i]] + mul[bel[i]] * inv(w[i]) % MOD + MOD) % MOD;
        }
        ans = (ans + i * res) % MOD;
    }
    printf("%I64d\n",ans);
}
int main(){
    int tt;
    for(scanf("%d",&tt); tt; tt--) solve();
    return 0;
}