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
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
#include <algorithm>
#include <bitset>
#include <cmath>
#include <cstdlib>
#include <ctime>
#include <deque>
#include <iostream>
#include <list>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <vector>

#include <unordered_set>
using namespace std;

#define JOIN_(X, Y) X##Y
#define JOIN(X, Y) JOIN_(X, Y)
#define TMP JOIN(tmp, __LINE__)
#define PB push_back
#define SZ(x) int((x).size())
#define REP(i, n) for (int i = 0, TMP = (n); i < TMP; ++i)
#define FOR(i, a, b) for (int i = (a), TMP = (b); i <= TMP; ++i)
#define FORD(i, a, b) for (int i = (a), TMP = (b); i >= TMP; --i)

#ifdef DEBUG
#define DEB(x) (cerr << x)
#else
#define DEB(x)
#endif

template <typename T> ostream &operator<<(ostream &os, const vector<T> &v) {
  os << "vector[";
  for (const auto &e : v) {
    os << e << ", ";
  }
  os << "]";
  return os;
}

typedef long long ll;
typedef vector<int> vi;
typedef pair<int, int> pii;
typedef unsigned int uint;

const int INF = 1e9 + 9;

struct Sieve {
  int n;
  vi primes;
  vector<bool> is_prime;

  void fill(int _n) {
    n = _n;
    primes.clear();
    is_prime.clear();
    is_prime.resize(n + 1, true);
    FOR(i, 2, sqrt(n) + 1) {
      if (is_prime[i]) {
        for (int j = i * 2; j <= n; j += i) {
          is_prime[j] = false;
        }
      }
    }
    FOR(i, 2, n) {
      if (is_prime[i]) {
        primes.PB(i);
      }
    }
  }
};

struct Case {
  int n, q;
  vi cnt_mod2;
  vector<bool> bits;
  Sieve sieve;
  unordered_set<int> current;
  vi cnt;

  void solve() {
    cin >> n >> q;

    sieve.fill(n);
#ifdef DEBUG
    DEB("primes:\n");
    for (int prime : sieve.primes) {
      DEB(prime << " ");
    }
    DEB("\n");
#endif

    cnt_mod2.resize(2);
    bits.resize(n + 1);
    REP(_, q) {
      int pos;
      cin >> pos;
      int prev_bit = int(bits[pos]);

      bits[pos].flip();
      if (bits[pos]) {
        current.emplace(pos);
      } else {
        current.erase(pos);
      }

      int next_bit = int(bits[pos]);
      int diff = next_bit - prev_bit;
      cnt_mod2[pos % 2] += diff;
      DEB("cnt_mod_2 = " << cnt_mod2 << "\n");

      cnt.resize(n + 1);
      int result = max(cnt_mod2[0], cnt_mod2[1]);
      result = max(result, get_result());
      cout << result << "\n";
    }
  }

  int get_result() {
    DEB("SZ(current) = " << SZ(current) << "\n");
    int min_result = SZ(current) / 2;
    DEB("min_result = " << min_result << "\n");

    if (SZ(current) <= 2) {
      return SZ(current);
    }

    int result = 0;
    for (int k : sieve.primes) {
      DEB("  k=" << k << " n / k = " << n / k
                 << " < min_result = " << min_result << "\n");
      if (n / k <= min_result) {
        break;
      }
      for (int x : current) {
        int cand = ++cnt[x % k];
        result = max(result, cand);
        min_result = max(min_result, result + 1);
        DEB("    cand = " << cand << " result = " << result << "\n");
      }
      for (int x : current) {
        cnt[x % k] = 0;
      }
    }
    return result;
  }
};

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int z = 1;
  // cin >> z;
  while (z--) {
    Case().solve();
  }
}