/*
ID: dzhouwave
PROG: closing
LANG: C++11
*/

// @BEGIN_OF_SOURCE_CODE

#include <bits/stdc++.h>

#define pi acos(-1.0)
#define LL unsigned long long
using namespace std;

//#define cin fin
//ifstream fin ("closing.in");
//#define cout fout
//ofstream fout ("closing.out");

vector<int> dsu;
vector<pair<int, int>> edges;
vector<int> positions;
vector<vector<int>> nodes;

int dsuFind(int input)
{
    if(dsu[input] == -1)
    {
        return input;
    }
    else
    {
//        dsu[input] = dsuFind(dsu[input]);
        return dsuFind(dsu[input]);
    }
}

int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    int N, M;
    cin >> N >> M;
//    cout << N << " " << M << endl;
    positions.resize(N);
    dsu.resize(N);
    fill(dsu.begin(), dsu.end(), -1);
    nodes.resize(N);
    for(int i = 0; i < M; i++)
    {
        int first, second;
        cin >> first >> second;
//        cout << first << " " << second << endl;
        edges.emplace_back(first-1, second-1);
    }
    for(int i = 0; i < N; i++)
    {
        int input;
        cin >> input;
//        cout << input << endl;
        positions[N-i-1] = input-1;
    }
    for(int i = 0; i < edges.size(); i++)
    {
        int first = positions[edges[i].first];
        int second = positions[edges[i].second];
//        cout << first << " " << second << endl;
        if(first < second)
        {
            nodes[edges[i].second].push_back(edges[i].first);
        }
        else
        {
            nodes[edges[i].first].push_back(edges[i].second);
        }
    }
//    for(int i = 0; i < nodes.size(); i++)
//    {
//        cout << i << endl;
//        for(int j = 0; j < nodes[i].size(); j++)
//        {
//            cout << nodes[i][j] << " ";
//        }
//        cout << endl;
//    }
//    cout << endl;
//    cout << endl;
//    cout << endl;

    queue<int> unconnected;
    vector<string> result;
    int comps = 0;
    for(int i = 0; i < positions.size(); i++)
    {
//        cout << positions[i] << endl;
        comps++;
        for(int j = 0; j < nodes[positions[i]].size(); j++)
        {
            int x = dsuFind(positions[i]);
            int y = dsuFind(nodes[positions[i]][j]);
            if(x == y)
            {
                //do nothing
            }
            else
            {
                dsu[x] = y;
                comps--;
//                dsuFind(positions[i]);
            }
//            cout << "UNIONIZING" << endl;
//            cout << positions[i] << " " << nodes[positions[i]][j] << endl;
//            cout << dsu[positions[i]] << " " << dsuFind(nodes[positions[i]][j]) << endl;
        }
        if(comps <= 1)
        {
            result.push_back("YES");
        }
        else
        {
            result.push_back("NO");
        }
    }
    for(int i = 0; i < result.size(); i++)
    {
        cout << result[result.size()-i-1] << endl;
    }
//    for(int i = 0; i < dsu.size(); i++)
//    {
//        cout << dsu[i] << endl;
//    }
    return 0;
}

// @END_OF_SOURCE_CODE