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#include <cstdio>
#include <cstdlib>
#include <cstdint>
#include <ctime>
#include <vector>
#include <set>
#include <queue>

using namespace std;

const int64_t MOD = 10000008;
const int FORCE_SMALL_PRIMES = 128;
const int RANDOM_SAMPLE_SIZE = 256;
const int FORCE_INITIAL = 64;
const int FORCE_INITIAL_DELTA = 8;
const int MAX_FULL_SEARCH_Q = 4096;
const int PQUE_REBUILD_INTERVAL = 4096;
const int SIEVE_MAX = 10000;

int main () {
	srand(time(0));
	int n, q;
	scanf("%d %d", &n, &q);
	vector<int> primes;
	vector<bool> is_prime(SIEVE_MAX, true);
	is_prime[0] = false;
	is_prime[1] = false;
	for (int i = 2; i < SIEVE_MAX; ++i) {
		if (is_prime[i]) {
			primes.push_back(i);
			int next = 2 * i;
			while (next < SIEVE_MAX) {
				is_prime[next] = false;
				next += i;
			}
		}
	}
	vector<int> changes(q, 0);
	for (int i = 0; i < q; ++i) {
		scanf("%d", &changes[i]);
	}
	set<int> deltas;
	if (q <= MAX_FULL_SEARCH_Q) {
		for (int i = 0; i < q - 1; ++i) {
			for (int j = i + 1; j < q; ++j) {
				deltas.insert(abs(changes[j] - changes[i]));
			}
		}
	}
	else {
		for (int i = 0; i < FORCE_INITIAL; ++i) {
			for (int j = 1; j <= FORCE_INITIAL_DELTA; ++j) {
				if (i + j >= q) {
					continue;
				}
				deltas.insert(abs(changes[i + j] - changes[i]));
			}
		}
		for (int i = 0; i < RANDOM_SAMPLE_SIZE; ++i) {
			deltas.insert(abs(changes[rand() % q] - changes[rand() % q]));
		}
	}
	set<int> primes_to_use;
	for (int i = 0; i < FORCE_SMALL_PRIMES; ++i) {
		primes_to_use.insert(primes[i]);
	}
	for (set<int>::iterator it = deltas.begin(); it != deltas.end(); it++) {
		if (*it < 2) {
			continue;
		}
		int test_div = 2;
		bool found = false;
		while (test_div * test_div <= *it) {
			if ((*it % test_div == 0) && is_prime[test_div]) {
				primes_to_use.insert(test_div);
				found = true;
			}
			++test_div;
		}
		if (!found) {
			primes_to_use.insert(*it);
		}
	}
	vector<int> primes_filtered;
	for (set<int>::iterator it = primes_to_use.begin(); it != primes_to_use.end(); it++) {
		primes_filtered.push_back(*it);
	}
	priority_queue<pair<int, int64_t> > pque;
	vector<vector<int> > counters;
	for (int i = 0; i < primes_filtered.size(); ++i) {
		counters.push_back(vector<int>(primes_filtered[i], 0));
	}
	vector<bool> enabled(n, false);
	for (int i = 0; i < q; ++i) {
		int x = changes[i];
		if (!enabled[x]) {
			enabled[x] = true;
			for (int j = 0; j < primes_filtered.size(); ++j) {
				int prime = primes_filtered[j];
				int64_t key = ((int64_t)j) * MOD + (int64_t)(x % prime);
				int cnt = ++counters[j][x % prime];
				pque.push(make_pair(cnt, key));
			}
		}
		else {
			enabled[x] = false;
			for (int j = 0; j < primes_filtered.size(); ++j) {
				int prime = primes_filtered[j];
				int64_t key = ((int64_t)j) * MOD + (int64_t)(x % prime);
				int cnt = --counters[j][x % prime];
				if (cnt) {
					pque.push(make_pair(cnt, key));
				}
			}
		}
		if (i % PQUE_REBUILD_INTERVAL == PQUE_REBUILD_INTERVAL - 1) {
			pque = priority_queue<pair<int, int64_t> >();
			for (int j = 0; j < counters.size(); ++j) {
				for (int k = 0; k < counters[j].size(); ++k) {
					int val = counters[j][k];
					if (val > 0) {
						pque.push(make_pair(counters[j][k], ((int64_t)j) * MOD + (int64_t)k));
					}
				}
			}
		}
		bool found = false;
		while (!pque.empty()) {
			pair<int, int64_t> item = pque.top();
			if (counters[item.second / MOD][item.second % MOD] == item.first) {
				printf("%d\n", item.first);
				found = true;
				break;
			}
			else {
				pque.pop();
			}
		}
		if (!found) {
			printf("0\n");
		}
	}
	return 0;
}