#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
const ll MAXN = 1e14;
const int MAXK = 25e4;
const int MAXF = 1e6;
ll n;
int k;
ll elems[MAXK];
ll gcd(ll a, ll b) {
if (a > b) return gcd(b, a);
if (a == 0) return b;
return gcd(b%a, a);
}
vector<ll> primes;
vector<ll> nprimes;
bool is_prime[(int) sqrt(MAXN)+1];
vector<pii> factorizations[MAXK];
int state[MAXF]; // 0 unvisited, 2 descended from k, 1 blocked
ll val[MAXF];
int hshs[MAXK];
int coeffs[MAXK];
int mxh = 0;
ll ans = 2;
void make_primes(ll mx) {
fill(is_prime, is_prime+mx+1, 1);
for (int i = 2; i <= mx; i++) {
if (!is_prime[i]) continue;
primes.push_back(i);
for (int j = 2*i; j <= mx; j+= i) is_prime[j] = 0;
}
}
void factorize(ll target, vector<pii> &factored) { // prime
for (int i = 0; i < primes.size() && target > 1; i++) {
int c = 0;
while (target % primes[i] == 0) {
target /= primes[i];
c++;
nprimes.push_back(primes[i]);
}
if (c) factored.push_back(pii(primes[i], c));
}
if (target != 1) {
nprimes.push_back(target);
factored.push_back(pii(target, 1));
}
}
void factorize2(ll target, vector<pii> &factored) { // prime
for (int i = 0; i < nprimes.size(); i++) {
int c = 0;
while (target % nprimes[i] == 0) {
target /= nprimes[i];
c++;
}
factored.push_back(pii(nprimes[i], c));
}
}
void make_coeffs() {
int mult = 1;
for (int i = 0; i < nprimes.size(); i++) {
coeffs[i] = mult;
mult *= (factorizations[k-1][i].second+1);
}
}
int hsh(vector<pii> &factored) {
int r = 0;
for (int i = 0; i < nprimes.size(); i++) {
r += factored[i].second*coeffs[i];
}
mxh = max(mxh, r);
return r;
}
int main() {
ios_base::sync_with_stdio(false); cin.tie(NULL);
cin >> n >> k;
for (int i = 0; i < k; i++) {
cin >> elems[i];
if (elems[i] == 0) elems[i] = n;
ans -= (elems[i] == n);
}
if (elems[i] == n && k < n) ans = 2;
elems[k-1] = gcd(elems[k-1], n);
for (int i = 0; i < k-1; i++) elems[i] = gcd(elems[i], elems[k-1]);
make_primes((int) sqrt(n));
factorize(elems[k-1], factorizations[k-1]);
make_coeffs();
hshs[k-1] = hsh(factorizations[k-1]);
state[hshs[k-1]] = 2;
val[hshs[k-1]] = elems[k-1];
for (int i = 0; i < k-1; i++) {
factorize2(elems[i], factorizations[i]);
hshs[i] = hsh(factorizations[i]);
state[hshs[i]] = 1;
val[hshs[i]] = elems[i];
}
for (int i = mxh; i >= 0; i--) {
if (state[i] == 0) continue;
if (state[i] == 2) ans = max(ans, n/val[i]);
for (int p = 0; p < nprimes.size(); p++) {
int v = i/coeffs[p];
if (v % (factorizations[k-1][p].second+1) == 0) continue;
int nxt = i-coeffs[p];
if (state[nxt] == 1 || (state[nxt] == 2 && state[i] == 2)) continue;
val[nxt] = val[i]/nprimes[p];
state[nxt] = state[i];
}
}
cout << ans << "\n";
}
Compilation message
sej.cpp: In function 'void factorize(ll, std::vector<std::pair<int, int> >&)':
sej.cpp:43:20: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
43 | for (int i = 0; i < primes.size() && target > 1; i++) {
| ~~^~~~~~~~~~~~~~~
sej.cpp: In function 'void factorize2(ll, std::vector<std::pair<int, int> >&)':
sej.cpp:59:20: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
59 | for (int i = 0; i < nprimes.size(); i++) {
| ~~^~~~~~~~~~~~~~~~
sej.cpp: In function 'void make_coeffs()':
sej.cpp:71:20: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
71 | for (int i = 0; i < nprimes.size(); i++) {
| ~~^~~~~~~~~~~~~~~~
sej.cpp: In function 'int hsh(std::vector<std::pair<int, int> >&)':
sej.cpp:79:20: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
79 | for (int i = 0; i < nprimes.size(); i++) {
| ~~^~~~~~~~~~~~~~~~
sej.cpp: In function 'int main()':
sej.cpp:94:12: error: 'i' was not declared in this scope
94 | if (elems[i] == n && k < n) ans = 2;
| ^
sej.cpp:112:21: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
112 | for (int p = 0; p < nprimes.size(); p++) {
| ~~^~~~~~~~~~~~~~~~
