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#include <algorithm>
#include <cassert>
#include <iostream>
#include <random>
#include <sched.h>
#include <set>
#include <vector>

using namespace std;
using ll = long long;
#define all(a) begin(a), end(a)

mt19937 rng{147852314};
int rand(int l, int r) { return uniform_int_distribution<>(l, r)(rng); }

constexpr int N = 1e7 + 10;
constexpr int X = 100;

int lp[N];

void init() {
    vector<int> primes(N);
    int ptr = 0;

    lp[1] = 1;
    for (int i = 2; i < N; ++i) {
        if (!lp[i]) {
            lp[i] = i;
            primes[ptr++] = i;
        }
        for (int it = 0; it < ptr; it++) {
            auto p = primes[it];
            int v = i * p;
            if (v >= N) {
                break;
            }

            lp[v] = p;
            if (p == lp[i]) {
                break;
            }
        }
    }
}

vector<int> get_primes(int n) {
    vector<int> res;
    while (n != 1) {
        int t = lp[n];
        res.push_back(t);
        while (n % t == 0) {
            n /= t;
        }
    }
    return res;
}

int cnt_buf[N];
vector<pair<pair<int, int>, int>> recalc(vector<int> const &a, int x, int lim) {
    assert(lim > 0);

    const int n = a.size();
    vector<int> ks{2};

    if (ll(n) * (n - 1) / 2 <= x) {
        for (int i = 0; i < n; i++) {
            for (int j = i + 1; j < n; j++) {
                ks.push_back(abs(a[i] - a[j]));
            }
        }
    } else {
        for (int iter = 0; iter < x; iter++) {
            int i = rand(0, n - 1), j = rand(0, n - 1);
            if (i == j) {
                iter--;
                continue;
            }

            ks.push_back(abs(a[i] - a[j]));
        }
    }

    sort(all(ks));
    ks.erase(unique(all(ks)), end(ks));

    vector<int> ks2;
    for (auto i : ks) {
        for (auto j : get_primes(i)) {
            ks2.push_back(j);
        }
    }

    ks = ks2;
    sort(all(ks));
    ks.erase(unique(all(ks)), end(ks));

    vector<pair<pair<int, int>, int>> res;
    for (auto k : ks) {
        if (k == 1) {
            continue;
        }

        for (auto i : a) {
            ++cnt_buf[i % k];
        }

        for (auto i : a) {
            int d = i % k;
            int &c = cnt_buf[d];
            if (c >= lim) {
                res.push_back({{k, d}, c});
            }
            c = 0;
        }
    }

    return res;
}

int pos[N];
int freq[N];
void solve() {
    int n, q;
    cin >> n >> q;

    for (int i = 0; i <= n; i++) {
        pos[i] = -1;
        freq[i] = 0;
    }
    int res = 0;

    vector<int> nums;
    vector<pair<pair<int, int>, int>> cnt;

    int scheduled = 0;
    for (int iter = 0; iter < q; iter++) {
        int x;
        cin >> x;

        int d;
        int &p = pos[x];
        if (p != -1) {
            pos[nums.back()] = p;
            swap(nums[p], nums.back());
            nums.pop_back();
            p = -1;
            d = -1;
        } else {
            p = nums.size();
            nums.push_back(x);
            d = +1;
        }

        for (auto &[p, v] : cnt) {
            auto [k, b] = p;
            if (x % k == b) {
                --freq[v];
                v += d;
                ++freq[v];
                res = max(res, v);
            }
        }

        const int s = nums.size();
        if (iter >= scheduled || s <= 1) {
            const int g = s / 3, t = s - 2 * g;
            while (res >= 0) {
                freq[res--] = 0;
            }

            cnt = recalc(nums, X, max(1, g - 1));

            res = 0;
            for (auto [_, v] : cnt) {
                freq[v]++;
                res = max(res, v);
            }

            scheduled = iter + t;
        }

        while (res && !freq[res]) {
            res--;
        }

        cout << res << "\n";
    }
}

int main() {
    init();
    ios_base::sync_with_stdio(0);
    cin.tie(0);

    int q = 1;
    // cin >> q;
    while (q--) {
        solve();
    }
}