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#include <bits/stdc++.h>
// #include <ext/pb_ds/assoc_container.hpp>

#define ALL(x) (x).begin(), (x).end()
#define SZ(x) ((int)(x).size())

using namespace std;
// using namespace __gnu_pbds;

#ifdef LOCAL
template<typename A, typename B>
auto&operator<<(auto&o,pair<A, B>p){return o<<"("<<p.first<<", "<<p.second<<")";}
auto operator<<(auto&o,auto x)->decltype(x.end(),o){o<<"{";int i=0;for(auto e:x)o<<&","[!i++]<<e;return o<<"}";}
#define debug(X...)cerr<<"["#X"]: ",[](auto...$){((cerr<<$<<"; "),...)<<endl;}(X)
#else
#define debug(...){}
#endif

#define DEBUG(...) do { if (do_debug_now) debug(__VA_ARGS__); } while (0)

using u32 = unsigned;
using i64 = long long;
using ll = long long;
using pii = pair<int, int>;
using pll = pair<i64, i64>;
using vi = vector<int>;
using vll = vector<i64>;

const int MAXN = 10'100'000;
const int MAXQ = 1'000'005;

set<int> all_values{-2, -1, MAXN - 100, MAXN - 99};
int prime_sieve[MAXN];
int cur_size;

int N, Q;

int query_val[MAXQ];
int query_delta[MAXQ];
bool do_debug_now = false;

deque<pii> awaiting_checks;
int num_prime_occurs[MAXN];
bool is_prime_important[MAXN];
int answers[MAXN];
int num_rem_occurs[MAXN];
int freq_array[MAXQ];
set<pii> unimportant_primes;

void Preproc() {
	iota(prime_sieve, prime_sieve + MAXN, 0);

	for (int p = 2; p < MAXN; ++p) {
		if (prime_sieve[p] != p) { continue; }
		for (int i = p; i < MAXN; i += p) {
			prime_sieve[i] = p;
		}
	}
}

void ProcessDelta(int a, int b, int delta) {
	if (a < 0 || b > N) { return; }
	int diff = b - a;
	assert(diff >= 1);
	while (diff > 1) {
		const int p = prime_sieve[diff];
		while (diff % p == 0) {
			diff /= p;
		}

		int &occ = num_prime_occurs[p];
		DEBUG(a, b, delta, p, occ);
		
		if (!is_prime_important[p]) {
			unimportant_primes.erase(pii{occ, p});
		}
		occ += delta;
		if (!is_prime_important[p]) {
			if (occ > cur_size / 4) {
				is_prime_important[p] = true;
				awaiting_checks.emplace_front(-1, p);
			} else if (occ) {
				unimportant_primes.emplace(occ, p);
			}
		}
	}
}

void ProcessWaypoint(int cur_qid, int p) {
	DEBUG("ProcessWaypoint", cur_qid, p, all_values);
	const int num_steps = cur_size;
	const int last_step = min(Q, cur_qid + num_steps);

	freq_array[0] = p;

	auto Add = [&](int x, int delta) {
		int &occ = num_rem_occurs[x];
		--freq_array[occ];
		occ += delta;
		++freq_array[occ];
	};

	for (int val : all_values) {
		Add(val % p, +1);
	}

	int cur_result = 0;
	for (int i = 0; i <= cur_size; ++i) {
		if (freq_array[i]) {
			cur_result = i;
		}
	}

	answers[cur_qid] = max(answers[cur_qid], cur_result);
	DEBUG(cur_qid, cur_result);
	for (int qid = cur_qid + 1; qid < last_step; ++qid) {
		const int val = query_val[qid];
		const int delta = query_delta[qid];
		Add(val % p, delta);

		++cur_result;
		while (!freq_array[cur_result]) {
			--cur_result;
		}
		DEBUG(qid, val, delta, cur_result);
		answers[qid] = max(answers[qid], cur_result);
	}

	for (int val : all_values) {
		num_rem_occurs[val % p] = 0;
	}
	for (int qid = cur_qid + 1; qid < last_step; ++qid) {
		num_rem_occurs[query_val[qid] % p] = 0;
	}
	for (int i = 0; i <= cur_result; ++i) {
		freq_array[i] = 0;
	}
}

int main() {
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	cout << fixed << setprecision(14);

	Preproc();
	debug("pre done");

	vector<pii> important_waypoints;
	
	cin >> N >> Q;
	for (int qid = 0; qid < Q; ++qid) {
		// do_debug_now = abs(qid - 541000) <= 10;

		int val;
		cin >> val;
		query_val[qid] = val;
		auto [iter, is_new] = all_values.insert(val);
		const int delta = (is_new ? (+1) : (-1));
		cur_size += delta;
		query_delta[qid] = delta;
		DEBUG(qid, val, delta, cur_size);

		int p1, p2, n1, n2;
		{
			auto piter = prev(iter);
			p1 = *piter;
			p2 = *prev(piter);
		}
		{
			auto niter = next(iter);
			n1 = *niter;
			n2 = *next(niter);
		}

		ProcessDelta(p2, n1, -delta);
		ProcessDelta(p1, n2, -delta);
		ProcessDelta(val, n2, delta);
		ProcessDelta(val, n1, delta);
		ProcessDelta(p1, val, delta);
		ProcessDelta(p2, val, delta);

		if (!is_new) {
			all_values.erase(iter);
		}

		while (!unimportant_primes.empty()) {
			auto last = prev(unimportant_primes.end());
			DEBUG(cur_size, *last);
			if (last->first <= cur_size / 4) { break; }
			const int p = last->second;
			unimportant_primes.erase(last);
			is_prime_important[p] = true;
			awaiting_checks.emplace_front(-1, p);
		}
		
		while (!awaiting_checks.empty()) {
			const auto [tm, p] = awaiting_checks.front();
			DEBUG(tm, p, num_prime_occurs[p]);
			if (tm > qid) { break; }
			awaiting_checks.pop_front();
			assert(is_prime_important[p] == true);

			if (num_prime_occurs[p] > cur_size / 4) {
				awaiting_checks.emplace_back(qid + cur_size, p);
				important_waypoints.emplace_back(qid, p);
				DEBUG("important", qid, p, cur_size);
			} else {
				is_prime_important[p] = false;
				if (num_prime_occurs[p]) {
					unimportant_primes.emplace(num_prime_occurs[p], p);
				}
			}
		}

		DEBUG(all_values);
		DEBUG(unimportant_primes);
	}

	DEBUG(important_waypoints);

	all_values.clear();
	cur_size = 0;
	int way_ptr = 0;

	for (int qid = 0; qid < Q; ++qid) {
		if (query_delta[qid] == (+1)) {
			all_values.insert(query_val[qid]);
		} else {
			all_values.erase(query_val[qid]);
		}
		cur_size += query_delta[qid];
		answers[qid] = max(answers[qid], (cur_size + 1) / 2);

		while (way_ptr < SZ(important_waypoints) && important_waypoints[way_ptr].first == qid) {
			ProcessWaypoint(qid, important_waypoints[way_ptr].second);
			++way_ptr;
		}
	}

	for (int qid = 0; qid < Q; ++qid) {
		cout << answers[qid] << "\n";
	}
}