#include<iostream>
#include<cstdio>
#include<cstring>
#include<string>
#include<vector>
#include<cmath>
#include<algorithm>
#include<map>
#include<queue>
#include<deque>
#include<iomanip>
#include<tuple>
#include<cassert>
#include<set>
#include<complex>
#include<numeric>
#include<functional>
#include<unordered_map>
#include<unordered_set>
using namespace std;
typedef long long int LL;
typedef pair<int,int> P;
typedef pair<LL,LL> LP;
const int INF=1<<30;
const LL MAX=1e9+7;

void array_show(int *array,int array_n,char middle=' '){
    for(int i=0;i<array_n;i++)printf("%d%c",array[i],(i!=array_n-1?middle:'\n'));
}
void array_show(LL *array,int array_n,char middle=' '){
    for(int i=0;i<array_n;i++)printf("%lld%c",array[i],(i!=array_n-1?middle:'\n'));
}
void array_show(vector<int> &vec_s,int vec_n=-1,char middle=' '){
    if(vec_n==-1)vec_n=vec_s.size();
    for(int i=0;i<vec_n;i++)printf("%d%c",vec_s[i],(i!=vec_n-1?middle:'\n'));
}
void array_show(vector<LL> &vec_s,int vec_n=-1,char middle=' '){
    if(vec_n==-1)vec_n=vec_s.size();
    for(int i=0;i<vec_n;i++)printf("%lld%c",vec_s[i],(i!=vec_n-1?middle:'\n'));
}
template<typename T> ostream& operator<<(ostream& os,const vector<T>& v1){
    int n=v1.size();
    for(int i=0;i<n;i++){
        if(i)os<<" ";
        os<<v1[i];
    }
    return os;
}
template<typename T1,typename T2> ostream& operator<<(ostream& os,const pair<T1,T2>& p){
    os<<p.first<<" "<<p.second;
    return os;
}
template<typename T> istream& operator>>(istream& is,vector<T>& v1){
    int n=v1.size();
    for(int i=0;i<n;i++)is>>v1[i];
    return is;
}

namespace sol{

    void solve(){
        int n,m;
        int i,j,k;
        int a,b,c;
        cin>>n;
        vector<P> v1;
        for(i=0;i<2*n;i++){
            cin>>a;
            v1.push_back({a,i});
        }
        sort(v1.begin(),v1.end());
        string ss(2*n,'(');
        for(i=0;i<n;i++){
            a=v1[i].second;
            ss[a]=')';
        }
        a=-1,b=0;
        bool flag=false;
        for(i=0;i<2*n;i++){
            if(ss[i]=='(')b++;
            else b--;
            if(b<0)flag=true;
            if(b==0){
                if(flag){
                    for(j=a+1;j<=i;j++){
                        if(ss[j]=='(')ss[j]=')';
                        else ss[j]='(';
                    }
                }
                a=i;
                flag=false;
            }
        }
        cout<<ss<<endl;
    }
}

int main(){
    sol::solve();
}
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define forn(i,x,n) for(int i = x;i <= n;++i)
typedef pair<int,int> pii;
#define forr(i,x,n) for(int i = n;i >= x;--i)
#define Angel_Dust ios::sync_with_stdio(0);cin.tie(0)
#define x first
#define y second

const int N = 105,MOD = 1e9+7;
pii edges[N * N];
int deg[N];

struct Mat
{
    int c[N][N];
    Mat()
    {
        memset(c,0,sizeof c);
    }
    Mat operator*(const Mat& r) const
    {
        Mat res;
        forn(i,1,N - 1) forn(j,1,N - 1) forn(k,1,N - 1) res.c[i][j] = (res.c[i][j] + 1ll*c[i][k] * r.c[k][j] % MOD) % MOD;
        return res;
    }
    void operator*(int r) 
    {
        forn(i,1,N - 1) forn(j,1,N - 1) c[i][j] = 1ll*c[i][j] * r % MOD;
    }
};

Mat qpow(Mat a,int b,int MOD)
{
    Mat res;forn(i,1,N - 1) res.c[i][i] = 1;
    while(b)
    {
        if(b & 1)   res = res * a;
        a = a * a;
        b >>= 1;
    }
    return res;
}

int qpow(int a,int b,int MOD)
{
    int res = 1;
    while(b)
    {
        if(b & 1)   res = 1ll * res * a % MOD;
        a = 1ll * a * a % MOD;
        b >>= 1;
    }
    return res;
}

int main()
{
    // freopen("D://OJCodes//TTT//in.txt","r",stdin);
    // freopen("D://OJCodes//TTT//out.txt","w",stdout);
    
    int n,m,k;scanf("%d%d%d",&n,&m,&k);
    Mat f,B;forn(i,1,n)   scanf("%d",&f.c[1][i]);

    forn(i,1,m)
    {
        int u,v;scanf("%d%d",&u,&v);
        ++deg[u];++deg[v];
        edges[i] = {u,v};
    }

    int m_2fact = qpow(m * 2,MOD - 2,MOD);
    
    forn(i,1,m)
    {
        int u = edges[i].x,v = edges[i].y;
        B.c[u][v] = m_2fact;
        B.c[v][u] = m_2fact;
    }

    forn(i,1,n) B.c[i][i] = (2 * m - deg[i]) * 1ll * m_2fact % MOD;
    

    B = qpow(B,k,MOD);
    f = f * B;
    forn(i,1,n) printf("%d\n",f.c[1][i]);


    // fclose(stdin);
    // fclose(stdout);
    return 0;
}
