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#include<bits/stdc++.h>
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/hash_policy.hpp>
 
#define pb push_back
#define ppb pop_back
#define eb emplace_back
#define ff first
#define ss second
#define turbo ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
#define mid ((l+r)/2)
#define midLL ((l+r)/2LL)
#define mide ((lo+hi)/2)
#define mideLL ((lo+hi)/2LL)
#define endl '\n'
#define random_shuffle shandom_ruffle
#define lowbit(x) x&(-x)
#define bits(x) __builtin_popcount(x) 
#define mins(se) (*se.begin())
#define maxs(se) (*--se.end())
#define all(x) x.begin(), x.end()
#define log2_floor(i) (i ? __builtin_clzll(1) - __builtin_clzll(i) : -1)
#define siz(cont) ((int)cont.size())
#define each(it, cont) for(auto &it : cont)
#define ein(cont) for(auto &it : cont) cin >> it;
#define mp(a, b) make_pair(a, b)
#define FOR(i, st, end) for (int i = st; i < end; i++)

using namespace std;

using ll = long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pli = pair<ll, int>;
using pil = pair<int, ll>;
using vll = vector<pll>;
using vii = vector<pii>;
using vi = vector<int>;
using vl = vector<ll>;
using vvl = vector<vl>;
using vvi = vector<vi>;
using vvii = vector<vii>;
using vli = vector<pli>;
using vvli = vector<vli>;
using vil = vector<pil>;
using vvil = vector<vil>;
using vc = vector<char>;
using vvc = vector<vector<char>>;
using vb = vector<bool>;
using vvb = vector<vb>;
using umapii = unordered_map<int, int>;
using vumapii = vector<umapii>;
using umapiumapii = unordered_map<int, umapii>;

using namespace __gnu_pbds;

template <class K, class V>
using fast_map = gp_hash_table<
    K, V,
    hash<K>,
    equal_to<K>,
    direct_mask_range_hashing<>,
    linear_probe_fn<>,
    hash_standard_resize_policy<
        hash_exponential_size_policy<>, 
        hash_load_check_resize_trigger<>, 
        true
    >
>;

template <class K>
using fast_set = gp_hash_table<
    K, null_type,
    hash<K>,
    equal_to<K>,
    direct_mask_range_hashing<>,
    linear_probe_fn<>,
    hash_standard_resize_policy<
        hash_exponential_size_policy<>, 
        hash_load_check_resize_trigger<>, 
        true
    >
>;

#ifdef JDKURWE
void err() { std::cout << "\n"; fflush(stdout); }
template<class T, class... Ts>
void err(T arg, Ts &... args) {
    std::cout << arg << ' ';
    err(args...);
}
#else 
void err() {}
template<class T, class... Ts>
void err(T arg, Ts &... args) {
    err(args...);
}
#endif

using namespace std;

ll n;
ll pot = 1;
vi sit, sit_ind;
vi pi;
vector<fast_map<int, int>> rcnt;
fast_map<int, int> top;
int best;
fast_set<int> kam_se;

vi q_sum, q, q_min;
constexpr int STTL = 2000;
int max_pi, rethink_strat=-1;
bool strat = false;
vi cnt_clearer;
fast_set<int> se_clearer;

void sito() {
    sit = sit_ind = vi(n+10);
    for (ll i = 2; i < n; i++)
        if (!sit[i]) {
            sit[i] = i;
            sit_ind[i] = siz(pi);
            pi.pb(i);
            for (ll j = i*i; j < n; j+=i)
                if (!sit[j])
                    sit[j] = i;

        }
}

fast_set<int> to_update;
void factor(int x) {
    if (x < 2)
        return;
    for (;x != 1; x/=sit[x])
        to_update.insert(sit[x]);
}

void map_add(int i, int r) {
    int tcnt = rcnt[i][r];
    top[tcnt]--;
    if (tcnt == best)
        best++;
    rcnt[i][r]++;
    top[tcnt+1]++;

    cnt_clearer[i]++;
    if (cnt_clearer[i] == 1)
        se_clearer.insert(i);
}

void map_rem(int i, int r) {
    int tcnt = rcnt[i][r];
    top[tcnt]--;
    if (!top[tcnt] and tcnt == best)
        best--;
    rcnt[i][r]--;
    top[tcnt-1]++;

    cnt_clearer[i]--;
    if (!cnt_clearer[i])
        se_clearer.erase(i);
}

void add(int x) {
    FOR(i, 0, siz(pi)) {
        if (pi[i] > max_pi)
            break;
        int r = x%pi[i];
        map_add(i, r);
    }
}

void rem(int x) {
    FOR(i, 0, siz(pi)) {
        if (pi[i] > max_pi)
            break;
        int r = x%pi[i];
        map_rem(i, r);
    }
}


void add_small_q(int x, fast_set<int> &kse=kam_se) {
    to_update.clear();
    for (auto it : kse)
        factor(abs(it-x));
    for (auto it : to_update) {
        int r = x%it;
        int old = rcnt[sit_ind[it]][r];
        if (old == 0)
            map_add(sit_ind[it], r);
        map_add(sit_ind[it], r);
    }
}

void rem_small_q(int x) {
    to_update.clear();
    for (auto it : kam_se)
        factor(abs(it-x));
    for (auto it : to_update) {
        int r = x%it;
        map_rem(sit_ind[it], r);
    }
}


void init_strat() {
    vb kam(n+1);
    int qq; cin >> qq;
    q = q_sum = q_min = vi(qq);
    set<pii> mi_se;
    int sum = 0;
    for (int i = 0; i < qq; i++) {
        cin >> q[i];
        if (!kam[q[i]]) {
            sum++;
            kam[q[i]] = true;
        }
        else {
            kam[q[i]] = false;
            sum--;
        }
        q_sum[i] = sum;
    }
    for (int i = siz(q)-1; i >= 0; i--) {
        mi_se.insert({q_sum[i], i});
        if (i+STTL < siz(q))
            mi_se.erase({q_sum[i+STTL], i+STTL});
        q_min[i] = mins(mi_se).ff;
    }
}

void clear_for_strat() {
    top.clear();
    best = 0;
    for (auto it : se_clearer) {
        rcnt[it].clear();
        cnt_clearer[it] = 0;
    }
    se_clearer.clear();
}

void switch_to_small() {
    clear_for_strat();
    fast_set<int> kam_copy;
    for (auto it : kam_se) {
        kam_copy.insert(it);
        add_small_q(it, kam_copy);
    }
}

void switch_to_big() {
    clear_for_strat();
    for (auto it : kam_se)
        add(it);
}

void rescale(int new_mx) {
    if (new_mx > max_pi) {
        int start = 0;
        while (start < siz(pi) and pi[start] <= max_pi)
            start++;
        max_pi = new_mx;
        for (int i = start; i < siz(pi); i++) {
            if (pi[i] > max_pi)
                break;
            for (auto it : kam_se) {
                int r = it%pi[i];
                map_add(i, r);
            }
        }
        return;
    }

    // scale down
    for (int i = siz(pi)-1; i >= 0 and pi[i] > new_mx; i--)
        if (cnt_clearer[i])
            for (auto it : kam_se) {
                int r = it%pi[i];
                map_rem(i, r);
            }
    max_pi = new_mx;
}

void strat_check(int i) {
    if (i < rethink_strat)
        return;
    if (strat) {
        if (q_min[i] >= STTL*2) {
            int lower = q_min[i]/2;
            int new_mx = (n+lower-1)/lower;
            rescale(new_mx);
            rethink_strat+=STTL;
        }
        else {
            switch_to_small();
            strat = false;
            rethink_strat += STTL;
        }
        return;
    }

    if (q_min[i] >= STTL*2) {
        max_pi = n/STTL;
        rethink_strat+=STTL;
        strat = true;
        switch_to_big();
    }
    else {
        rethink_strat+=100;
    }
}

signed main() { 
    turbo;
    cin >> n;
    sito();
    rcnt = vector<fast_map<int, int>>(siz(pi));
    best = 0;
    q_sum = vi(q);
    cnt_clearer = vi(siz(pi));
    init_strat();
    rethink_strat = STTL;

    for (int i = 0; i < siz(q); i++) {
        int x = q[i];
        if (kam_se.find(x) != kam_se.end()) {
            kam_se.erase(x);
            if (strat)
                rem(x);
            else
                rem_small_q(x);
        }
        else {
            kam_se.insert(x);
            if (strat)
                add(x);
            else 
                add_small_q(x);
        }
        if (best == 0 and !kam_se.empty())
            cout << 1 << endl;
        else if (kam_se.empty())
            cout << 0 << endl;
        else 
            cout << best << endl;
        if (i == rethink_strat)
            strat_check(i);
    }
}