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

const int N = 1e7 + 10;
int pf[N];
vector<int> primes;

int K = 0;
int active[N];
int where[N];

const int M = 200;
int mod_count[M][2000];
int mem[25'000'000];
int *count_of_count[M];
int highest_count[M];

int C = 1;
int mark[N];
int current_count[N];

mt19937_64 gen(987);

int main() {
    cin.tie(0)->sync_with_stdio(0);

    auto T0 = clock();

    memset(where, -1, sizeof where);

    iota(pf, pf+N, 0);
    for (int i = 2; i < N; i++) if (pf[i] == i) {
        primes.push_back(i);
        if (i > N/i + 1) continue;
        for (int j = i*i; j < N; j += i) pf[j] = min(pf[j], i);
    }
    primes.resize(M);

    auto T1 = clock();
    cerr << fixed << setprecision(6);
    cerr << "Sieve:  " << double(T1-T0) / CLOCKS_PER_SEC << '\n';

    count_of_count[0] = mem;
    for (int i = 0; i+1 < M; i++) {
        int p = primes[i];
        count_of_count[i+1] = count_of_count[i] + 1 + (N+p-1) / p;
    }

    int n, q;
    cin >> n >> q;
    vector<int> xs(q);
    for (int &x: xs) cin >> x;

    auto update = [&](int x, bool skip_M = false) -> int {
        bool insert = where[x] < 0;
        if (insert) {
            active[K] = x;
            where[x] = K++;
        } else {
            int i = where[x];
            int y = active[--K];
            active[i] = y;
            where[y] = i;
            where[x] = -1;
        }

        if (skip_M) return 0;

        int res = 0;
        for (int i = 0; i < M; i++) {
            int p = primes[i], r = x % p;
            int &c = mod_count[i][r];
            assert(c >= 0);
            count_of_count[i][c]--;
            c += insert ? 1 : -1;
            count_of_count[i][c]++;
            if (insert) {
                if (highest_count[i] == c-1) highest_count[i]++;
            } else {
                if (count_of_count[i][highest_count[i]] == 0) highest_count[i]--;
            }
            res = max(res, highest_count[i]);
        }
        assert(res >= K/2);
        return res;
    };

    vector<vector<tuple<int,int,int>>> best(q);
    vector<int> res(q);
    for (int t = 0; t < q; t++) {
        res[t] = update(xs[t]);

        if (K <= 1) continue;

        set<int> done;
        auto consider = [&](int p) {
            if (p <= primes[M-1]) return;
            if (res[t] >= (n+p-1)/p) return;
            if (done.count(p)) return;
            done.insert(p);

            set<int> ys;

            for (int k = 0; k < K; k++) {
                int y = active[k] % p;
                if (mark[y] != C) current_count[y] = 0, mark[y] = C;
                if (++current_count[y] > K/3) ys.insert(y);
            }
            for (int y: ys) {
                best[t].emplace_back(p, y, current_count[y]);
                res[t] = max(res[t], current_count[y]);
            }
            C++;
        };

        int Z = max(3, min(30, 100/K));
        for (int z = 0; z < Z; z++) {
            int i = gen() % K, j = gen() % K;
            while (j == i) j = gen() % K;
            for (int x = abs(active[j]-active[i]); x > 1; x /= pf[x]) {
                if (pf[x] != pf[x/pf[x]]) consider(pf[x]);
            }
        }
    }

    auto make_unique = [&](auto &v) {
        sort(begin(v), end(v));
        auto it = unique(begin(v), end(v));
        v.erase(it, end(v));
    };

    for (int t = q-1; t >= 0; t--) {
        make_unique(best[t]);
        for (auto tpl: best[t]) res[t] = max(res[t], get<2>(tpl));

        int x = xs[t];
        bool insert = where[x] < 0;
        update(x, true);

        if (t > 0) {
            for (auto [p, y, c]: best[t]) {
                c += (insert ? 1 : -1) * (x%p == y);
                if (c > K/3) best[t-1].emplace_back(p, y, c);
            }
        }
    }
    
    auto T2 = clock();
    cerr << "Pass 1: " << double(T2-T1) / CLOCKS_PER_SEC << '\n';

    for (int t = 0; t < q; t++) {
        int x = xs[t];
        bool insert = where[x] < 0;
        update(x, true);

        if (t > 0) {
            for (auto [p, y, c]: best[t-1]) {
                c += (insert ? 1 : -1) * (x%p == y);
                if (c > K/3) best[t].emplace_back(p, y, c);
            }
        }

        make_unique(best[t]);
        for (auto tpl: best[t]) res[t] = max(res[t], get<2>(tpl));
    }
    
    auto T3 = clock();
    cerr << "Pass 2: " << double(T3-T2) / CLOCKS_PER_SEC << '\n';

    for (int k: res) cout << k << '\n';
}