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#include <bits/stdc++.h>
using namespace std;

#define pb push_back
#define fi first
#define sn second

typedef long long ll;
typedef vector<int> VI;
typedef vector<bool> VB;
typedef vector<char> VC;
typedef pair<int, int> PI;


struct Candidate {
    int prime;
    int rest;
    int time;
    int val;
};

bool operator<(Candidate a, Candidate b) {
    return a.val < b.val;
}


int main() {
    int n, q;
    cin >> n >> q;

    VB is_prime(n, true);
    if (n > 0) is_prime[0] = false;
    if (n > 1) is_prime[1] = false;

    for (ll i = 2; i * i < n; i++) {
        if (is_prime[i]) {
            for (ll j = i * i; j < n; j += i) {
                is_prime[j] = false;
            }
        }
    }

    VI primes;

    vector<VI> rests;
    vector<VI> updated;

    priority_queue<Candidate> Q;
    unordered_map<int, bool> D;

    for (int i = 2; i < n; i++) {
        if (is_prime[i]) {
            primes.pb(i);
            // prime_to_idx[i] = (int)primes.size();
            rests.pb(VI(i, 0));
            updated.pb(VI(i, 0));
        }
    }

#ifdef DEBUG
    cout << primes.size() << endl;
    for (int j = 0; j < primes.size(); j++) {
        cout << primes[j] << " ";
    }
    cout << endl;
#endif

    int x;
    for (int i = 1; i <= q; i++) {
        cin >> x;
        // x--;

        int dif = -1;

        if (!D[x]) {
            dif = 1;
            D[x] = true;
        }
        else {
            D[x] = false;
        }

        // cout << "Diff: " << x << " + " << dif << endl;

        for (int j = 0; j < primes.size(); j++) {
            int mod = x % primes[j];


            rests[j][mod] += dif;
            updated[j][mod] = i + 1;



            Candidate c;
            c.prime = j;
            c.rest = mod;
            c.time = i + 1;
            c.val = rests[j][mod];

            Q.push(c);
        }

#ifdef DEBUG

        for (int j = 0; j < primes.size(); j++) {
            cout << "P: " << primes[j] << endl;

            for (int k = 0; k < primes[j]; k++) {
                cout << " " << k << " ";
            }
            cout << endl;
            for (int k = 0; k < primes[j]; k++) {
                cout << " " << rests[j][k] << " ";
            }
            cout << endl;
        }
#endif

        while (!Q.empty()) {
            Candidate c = Q.top();
            if (updated[c.prime][c.rest] > c.time) {
                // cout << "POP " << c.prime << " " << c.rest << endl;
                Q.pop();
            }
            else {
                break;
            }
        }

        cout << Q.top().val << endl;
#ifdef DEBUG
        // cout << Q.top().val << " " << primes[Q.top().prime] << endl;
        if (x == 2) {
            while (!Q.empty()) {
                cout << Q.top().val << " " << primes[Q.top().prime] << endl;
                Q.pop();
            }
            break;
        }
#endif

    }


    return 0;
}