#include <bits/stdc++.h>
using namespace std;
#define rep(i, a, b) for (int i = (a); i < (b); i++)
#define all(x) begin(x), end(x)
#define sz(x) int((x).size())
using ll = long long;
using pii = pair<int, int>;
using vi = vector<int>;
#ifdef LOCAL
auto operator<<(auto& o, auto x) -> decltype(x.first, o);
auto operator<<(auto& o, auto x) -> decltype(x.end(), o) {
o << "{";
for (int i = 0; auto y : x) o << ", " + !i++ * 2 << y;
return o << "}"; }
auto operator<<(auto& o, auto x) -> decltype(x.first, o) {
return o << "(" << x.first << ", " << x.second << ")"; }
void __print(auto... x) { ((cerr << x << " "), ...) << endl; }
#define debug(x...) __print("[" #x "]:", x)
#else
#define debug(...) 2137
#endif
const int N = 50050;
int n, s;
int a[N], b[N];
vector<array<int, 3>> odp;
int id;
int suma(int x, int y) {
odp.push_back({1, x, y});
return id++;
}
int prz(int x, int y) {
odp.push_back({2, x, y});
return id++;
}
int neg(int x) {
odp.push_back({3, x, 0});
return id++;
}
#ifdef LOCAL
using B = bitset<N>;
void spr() {
vector<B> v;
int m = sz(odp);
v.resize(n + m);
rep(i, 0, n) {
for (int j = i + 1; j <= n; j += i + 1) v[i][j] = 1;
}
rep(i, 0, m) {
auto [t, x, y] = odp[i];
if (t == 1) {
x--; y--;
v[n + i] = v[x] | v[y];
} else if (t == 2) {
x--; y--;
v[n + i] = v[x] & v[y];
} else {
x--;
v[n + i] = ~v[x];
}
}
rep(i, 1, n + 1) {
assert(v[n + m - 1][i] == b[i]);
}
}
#endif
int main() {
cin.tie(0)->sync_with_stdio(0);
cin >> n >> s;
int fi = n;
rep(i, 0, s) {
int x;
cin >> x;
b[x] = 1;
fi = min(fi, x);
}
id = n + 1;
int t = suma(fi, fi);
for (int i = fi; i <= n; i += fi) a[i] = 1;
rep(i, fi + 1, n + 1) {
if (a[i] == 1 && b[i] == 0) {
t = prz(t, neg(i));
for (int j = i; j <= n; j += i) a[j] = 0;
} else if (a[i] == 0 && b[i] == 1) {
t = suma(t, i);
for (int j = i; j <= n; j += i) a[j] = 1;
}
}
assert(sz(odp) <= 100'000);
cout << sz(odp) << '\n';
for (auto [x, y, z] : odp) {
cout << x << ' ' << y;
if (x != 3) cout << ' ' << z;
cout << '\n';
}
#ifdef LOCAL
spr();
#endif
}
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 | #include <bits/stdc++.h> using namespace std; #define rep(i, a, b) for (int i = (a); i < (b); i++) #define all(x) begin(x), end(x) #define sz(x) int((x).size()) using ll = long long; using pii = pair<int, int>; using vi = vector<int>; #ifdef LOCAL auto operator<<(auto& o, auto x) -> decltype(x.first, o); auto operator<<(auto& o, auto x) -> decltype(x.end(), o) { o << "{"; for (int i = 0; auto y : x) o << ", " + !i++ * 2 << y; return o << "}"; } auto operator<<(auto& o, auto x) -> decltype(x.first, o) { return o << "(" << x.first << ", " << x.second << ")"; } void __print(auto... x) { ((cerr << x << " "), ...) << endl; } #define debug(x...) __print("[" #x "]:", x) #else #define debug(...) 2137 #endif const int N = 50050; int n, s; int a[N], b[N]; vector<array<int, 3>> odp; int id; int suma(int x, int y) { odp.push_back({1, x, y}); return id++; } int prz(int x, int y) { odp.push_back({2, x, y}); return id++; } int neg(int x) { odp.push_back({3, x, 0}); return id++; } #ifdef LOCAL using B = bitset<N>; void spr() { vector<B> v; int m = sz(odp); v.resize(n + m); rep(i, 0, n) { for (int j = i + 1; j <= n; j += i + 1) v[i][j] = 1; } rep(i, 0, m) { auto [t, x, y] = odp[i]; if (t == 1) { x--; y--; v[n + i] = v[x] | v[y]; } else if (t == 2) { x--; y--; v[n + i] = v[x] & v[y]; } else { x--; v[n + i] = ~v[x]; } } rep(i, 1, n + 1) { assert(v[n + m - 1][i] == b[i]); } } #endif int main() { cin.tie(0)->sync_with_stdio(0); cin >> n >> s; int fi = n; rep(i, 0, s) { int x; cin >> x; b[x] = 1; fi = min(fi, x); } id = n + 1; int t = suma(fi, fi); for (int i = fi; i <= n; i += fi) a[i] = 1; rep(i, fi + 1, n + 1) { if (a[i] == 1 && b[i] == 0) { t = prz(t, neg(i)); for (int j = i; j <= n; j += i) a[j] = 0; } else if (a[i] == 0 && b[i] == 1) { t = suma(t, i); for (int j = i; j <= n; j += i) a[j] = 1; } } assert(sz(odp) <= 100'000); cout << sz(odp) << '\n'; for (auto [x, y, z] : odp) { cout << x << ' ' << y; if (x != 3) cout << ' ' << z; cout << '\n'; } #ifdef LOCAL spr(); #endif } |
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