1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
#include <bits/stdc++.h>

using namespace std;

const int MAX_N = 10'000'007;
const int MAX_PRIMES = 700'005;

#ifndef HYBRID_D_THRESHOLD
#define HYBRID_D_THRESHOLD 200
#endif

vector<int> T;
int pos_T[MAX_N];
int cand[MAX_N];

long long n, q;
vector<int> spf;
vector<int> primes;
vector<int> candidates_buf;
vector<int> touched_mods;
vector<int> seen_prime_epoch;
int curr_query = 1;

long long d = 0;

void gen_primes() {
    spf.resize(n + 1, 0);
    seen_prime_epoch.resize(n + 1, 0);
    primes.reserve(MAX_PRIMES);

    for (int i = 2; i <= n; ++i) {
        if (spf[i] == 0) {
            spf[i] = i;
            primes.push_back(i);
        }
        for (int p : primes) {
            long long v = p;
            v *= i;
            if (v > n || p > spf[i]) break;
            spf[v] = p;
        }
    }
}

void check_prime_candidate(int p) {
    if (seen_prime_epoch[p] == curr_query) return;
    seen_prime_epoch[p] = curr_query;
    candidates_buf.push_back(p);
}

void process_modulo(int k, long long &output) {
    touched_mods.clear();

    for (int val : T) {
        int rem = val % k;
        if (cand[rem] == 0) touched_mods.push_back(rem);
        ++cand[rem];
        if (cand[rem] > output) output = cand[rem];
    }

    for (int rem : touched_mods) cand[rem] = 0;
}

void solve() {
    if (d == 0) {
        cout << 0 << '\n';
        return;
    }

    long long output = 1;

    if (d < HYBRID_D_THRESHOLD) {
        ++curr_query;

        candidates_buf.clear();

        int m = T.size();
        for (int i = 0; i < m; ++i) {
            for (int j = i + 1; j < m; ++j) {
                int diff = abs(T[i] - T[j]);
                int tmp = diff;

                while (tmp > 1) {
                    int p = spf[tmp];
                    if (d * p <= 2 * n) check_prime_candidate(p);
                    while (tmp % p == 0) tmp /= p;
                }
            }
        }

        for (int k : candidates_buf) process_modulo(k, output);

        cout << output << '\n';
        return;
    }

    for (auto k: primes) {
        if (d * k > 2 * n) break;
        process_modulo(k, output);
    }

    cout << output << '\n';
}


int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);

    for (int i = 0; i < MAX_N; ++i) pos_T[i] = -1;
    
    cin >> n >> q;
    candidates_buf.reserve(HYBRID_D_THRESHOLD * HYBRID_D_THRESHOLD);
    gen_primes();

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

        if (pos_T[x] != -1) {
            int idx = pos_T[x];
            int last_val = T.back();

            T[idx] = last_val;
            pos_T[last_val] = idx;

            T.pop_back();
            pos_T[x] = -1;
            --d;
        }
        else {
            pos_T[x] = T.size();
            T.push_back(x);
            ++d;
        }

        solve();
    }

    return 0;
}