QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#516648 | #9167. Coprime Array | rogi52 | AC ✓ | 0ms | 3816kb | C++17 | 18.4kb | 2024-08-12 20:04:18 | 2024-08-12 20:04:18 |
Judging History
answer
#line 2 "cp-library/src/cp-template.hpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
using i32 = int;
using u32 = unsigned int;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
template < class T > bool chmin(T& a, T b) { if(a > b) { a = b; return true; } return false; }
template < class T > bool chmax(T& a, T b) { if(a < b) { a = b; return true; } return false; }
template < class T, class U > T ceil (T x, U y) { return (x > 0 ? (x + y - 1) / y : x / y); }
template < class T, class U > T floor(T x, U y) { return (x > 0 ? x / y : (x - y + 1) / y); }
int popcnt(i32 x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(i64 x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
#line 2 "cp-library/src/utility/rep_itr.hpp"
template < class T > struct itr_rep {
T i, d;
constexpr itr_rep(const T i) noexcept : i(i), d(1) {}
constexpr itr_rep(const T i, const T d) noexcept : i(i), d(d) {}
void operator++() noexcept { i += d; }
constexpr int operator*() const noexcept { return i; }
constexpr bool operator!=(const itr_rep x) const noexcept { return d > 0 ? i < x.i : i > x.i; }
};
template < class T > struct rep {
const itr_rep< T > s, t;
constexpr rep(const T t) noexcept : s(0), t(t) {}
constexpr rep(const T s, const T t) noexcept : s(s), t(t) {}
constexpr rep(const T s, const T t, const T d) noexcept : s(s, d), t(t, d) {}
constexpr auto begin() const noexcept { return s; }
constexpr auto end () const noexcept { return t; }
};
template < class T > struct revrep {
const itr_rep < T > s, t;
constexpr revrep(const T t) noexcept : s(t - 1, -1), t(-1, -1) {}
constexpr revrep(const T s, const T t) noexcept : s(t - 1, -1), t(s - 1, -1) {}
constexpr revrep(const T s, const T t, const T d) noexcept : s(t - 1, -d), t(s - 1, -d) {}
constexpr auto begin() const noexcept { return s; }
constexpr auto end () const noexcept { return t; }
};
#line 3 "cp-library/src/utility/io.hpp"
/* 128bit integer */
istream& operator>>(istream& is, i128& x) {
std::string s; is >> s;
int pm = (s[0] == '-');
x = 0;
for(int i : rep(pm, int(s.size()))) x = x * 10 + (s[i] - '0');
if(pm) x *= -1;
return is;
}
ostream& operator<<(ostream& os, const i128& x) {
if(x == 0) return os << '0';
i128 y = x;
if(y < 0) { os << '-'; y *= -1; }
std::vector<int> ny;
while(y > 0) { ny.push_back(y % 10); y /= 10; }
for(int i : revrep(ny.size())) os << ny[i];
return os;
}
template < class S, class T > istream& operator>>(istream& is, std::pair< S, T >& x) { is >> x.first >> x.second; return is; }
template < class S, class T > ostream& operator<<(ostream& os, const std::pair< S, T >& x) { os << x.first << " " << x.second; return os; }
namespace scanner {
struct sca {
template < class T > operator T() {
T s; std::cin >> s; return s;
}
};
struct vec {
int n;
vec(int n) : n(n) {}
template < class T > operator std::vector< T >() {
std::vector< T > v(n);
for(T& x : v) std::cin >> x;
return v;
}
};
struct mat {
int h, w;
mat(int h, int w) : h(h), w(w) {}
template < class T > operator std::vector< std::vector< T > >() {
std::vector m(h, std::vector< T >(w));
for(std::vector< T >& v : m) for(T& x : v) std::cin >> x;
return m;
}
};
struct speedup {
speedup() {
std::cin.tie(0);
std::ios::sync_with_stdio(0);
}
} speedup_instance;
}
scanner::sca in() { return scanner::sca(); }
scanner::vec in(int n) { return scanner::vec(n); }
scanner::mat in(int h, int w) { return scanner::mat(h, w); }
namespace printer {
void precision(int d) { std::cout << std::fixed << std::setprecision(d); }
void flush() { std::cout.flush(); }
}
template < class T >
ostream& operator<<(ostream& os, const std::vector< T > a) {
int n = a.size();
for(int i : rep(n)) { os << a[i]; if(i != n - 1) os << ' '; }
return os;
}
int print() { std::cout << '\n'; return 0; }
template < class head, class... tail > int print(head&& h, tail&&... t) {
std::cout << h; if(sizeof...(tail)) std::cout << ' ';
return print(std::forward<tail>(t)...);
}
template < class T > int print_n(const std::vector< T > a) {
int n = a.size();
for(int i : rep(n)) std::cout << a[i] << "\n";
return 0;
}
#line 2 "cp-library/src/utility/key_val.hpp"
template < class K, class V >
struct key_val {
K key; V val;
key_val() {}
key_val(K key, V val) : key(key), val(val) {}
template < std::size_t Index >
std::tuple_element_t< Index, key_val >& get() {
if constexpr (Index == 0) return key;
if constexpr (Index == 1) return val;
}
};
namespace std {
template < class K, class V > struct tuple_size < key_val< K, V > > : integral_constant< size_t, 2 > {};
template < class K, class V > struct tuple_element < 0, key_val< K, V > > { using type = K; };
template < class K, class V > struct tuple_element < 1, key_val< K, V > > { using type = V; };
}
#line 2 "cp-library/src/utility/vec_op.hpp"
template < class T > key_val< int, T > max_of(const vector< T >& a) {
int i = std::max_element(a.begin(), a.end()) - a.begin();
return {i, a[i]};
}
template < class T > key_val< int, T > min_of(const vector< T >& a) {
int i = std::min_element(a.begin(), a.end()) - a.begin();
return {i, a[i]};
}
template < class S, class T > S sum_of(const vector< T >& a) {
S sum = 0;
for(const T x : a) sum += x;
return sum;
}
template < class S, class T > vector< S > freq_of(const vector< T >& a, T L, T R) {
vector< S > res(R - L, S(0));
for(const T x : a) res[x - L] += 1;
return res;
}
template < class S, class T > struct prefix_sum {
vector< S > s;
prefix_sum(const vector< T >& a) : s(a) {
s.insert(s.begin(), S(0));
for(int i : rep(a.size())) s[i + 1] += s[i];
}
// [L, R)
S sum(int L, int R) { return s[R] - s[L]; }
};
#line 3 "cp-library/src/utility/heap.hpp"
template < class T > using heap_min = std::priority_queue< T, std::vector< T >, std::greater< T > >;
template < class T > using heap_max = std::priority_queue< T, std::vector< T >, std::less< T > >;
#line 27 "cp-library/src/cp-template.hpp"
#line 1 "cp-library/src/algorithm/bin_search.hpp"
template < class T, class F >
T bin_search(T ok, T ng, F f) {
while(abs(ng - ok) > 1) {
T mid = (ok + ng) / 2;
(f(mid) ? ok : ng) = mid;
}
return ok;
}
template < class T, class F >
T bin_search_real(T ok, T ng, F f, int step = 80) {
while(step--) {
T mid = (ok + ng) / 2;
(f(mid) ? ok : ng) = mid;
}
return ok;
}
#line 2 "cp-library/src/algorithm/argsort.hpp"
template < class T > std::vector< int > argsort(const std::vector< T > &a) {
std::vector< int > ids((int)a.size());
std::iota(ids.begin(), ids.end(), 0);
std::sort(ids.begin(), ids.end(), [&](int i, int j) {
return a[i] < a[j] || (a[i] == a[j] && i < j);
});
return ids;
}
#line 1 "macro.hpp"
namespace macro {
using size_type = int;
template < class container > void sort(container& a) { std::sort(std:: begin(a), std:: end(a)); }
template < class container > void rsort(container& a) { std::sort(std::rbegin(a), std::rend(a)); }
template < class container > void reverse(container& a) { std::reverse(std::begin(a), std::end(a)); }
template < class container > void unique(container& a) {
std::sort(std::begin(a), std::end(a));
a.erase(std::unique(std::begin(a), std::end(a)), std::end(a));
}
template < class container > container sorted(const container& a) { container b = a; sort(b); return std::move(b); }
template < class container > container rsorted(const container& a) { container b = a; rsort(b); return std::move(b); }
template < class container, class compare > void sort(container& a, const compare& cmp) { std::sort(std::begin(a), std::end(a), cmp); }
template < class container, class compare > container sorted(const container& a, const compare& cmp) { container b = a; sort(b, cmp); return std::move(b); }
template < class container, class value > size_type lower_bound(const container& a, const value& x) { return std::lower_bound(std::begin(a), std::end(a), x) - std::begin(a); }
template < class container, class value > size_type upper_bound(const container& a, const value& x) { return std::upper_bound(std::begin(a), std::end(a), x) - std::begin(a); }
const std::vector<std::pair<size_type, size_type>> dir4 = { {+1, 0}, {-1, 0}, { 0, +1}, { 0, -1} };
const std::vector<std::pair<size_type, size_type>> dir8 = { {-1, -1}, {-1, 0}, {-1, +1}, { 0, -1}, { 0, +1}, {+1, -1}, {+1, 0}, {+1, +1} };
#ifdef _DEBUG
#define debug(x) std::cout << "[" << __LINE__ << "] " << #x << ": " << x << std::endl
#else
#define debug(x)
#endif
template < class container > void concat(container& a, const container& b) {
a.insert(std::end(a), std::begin(b), std::end(b));
}
std::vector<size_type> iota(const size_type n) {
std::vector<size_type> I(n);
std::iota(std::begin(I), std::end(I), 0);
return I;
}
template < class container > std::vector<size_type> sort_idx(const container& a) {
const size_type n = a.size();
std::vector<size_type> I = iota(n);
std::sort(std::begin(I), std::end(I), [&](size_type i, size_type j) { return a[i] < a[j] or (a[i] == a[j] and i < j); });
return I;
}
template < class container, class compare > std::vector<size_type> sort_idx(const container& a, const compare& cmp) {
const size_type n = a.size();
std::vector<size_type> I = iota(n);
std::sort(std::begin(I), std::end(I), [&](size_type i, size_type j) { return cmp(a[i], a[j]) or (a[i] == a[j] and i < j); });
return std::move(I);
}
struct grid {
using size_type = int;
size_type H, W;
grid(const size_type H, const size_type W) : H(H), W(W) {}
bool contains(const size_type i, const size_type j) {
return 0 <= i and i < H and 0 <= j and j < W;
}
};
using f64 = long double;
template < class T > vector< T >& operator++(vector< T >& a) { for(T& x : a) x++; return a; }
template < class T > vector< T >& operator--(vector< T >& a) { for(T& x : a) x--; return a; }
template < class T > vector< T > operator++(vector< T >& a, signed) { vector< T > res = a; for(T& x : a) x++; return res; }
template < class T > vector< T > operator--(vector< T >& a, signed) { vector< T > res = a; for(T& x : a) x--; return res; }
} // namespace macro
using namespace macro;
#line 1 "cp-library/src/number/crt.hpp"
// ax + by = gcd(a,b)
// return (x, y, gcd(a,b)) [min(|x|+|y|), x<=y]
template < class Int > std::tuple<Int, Int, Int> ext_gcd(Int a, Int b) {
if(b == 0) return {1, 0, a};
auto [s, t, g] = ext_gcd(b, a % b); // bs + (a%b)t = g
// ax + by = g
// <=> ((a/b)b + (a%b))x + by = g
// <=> b((a/b)x + y) + (a%b)x = g
return {t, s - (a / b) * t, g};
}
// 0 <= x < m
template < class Int > Int safe_mod(Int x, Int m) {
x %= m;
if(x < 0) x += m;
return x;
}
// x = r[i] (mod m[i])
template < class Int > std::pair<Int, Int> crt(std::vector<Int> r, std::vector<Int> m) {
assert(r.size() == m.size());
const int n = r.size();
auto [r0, m0] = std::make_pair<Int, Int>(0, 1);
for(int i = 0; i < n; i++) {
auto [r1, m1] = std::make_pair(safe_mod(r[i], m[i]), m[i]);
if(m0 < m1) {
std::swap(r0, r1);
std::swap(m0, m1);
}
if(m0 % m1 == 0) {
if(r0 % m1 != r1) return {0, 0};
continue;
}
auto [im, _, g] = ext_gcd(m0, m1);
if((r1 - r0) % g != 0) return {0, 0};
Int u = m1 / g;
r0 += (r1 - r0) / g % u * im % u * m0;
m0 *= u;
if(r0 < 0) r0 += m0;
}
return {r0, m0};
}
template < class Int > Int mod_inv(Int a, Int m) {
auto [ia, _, g] = ext_gcd(a, m);
return safe_mod(ia, m);
}
// x = r[i] (mod m[i])
// return (x mod M, lcm(m) mod M)
template < class Int > std::pair<Int, Int> garner(std::vector<Int> r, std::vector<Int> m, Int M, bool coprime) {
assert(r.size() == m.size());
const int n = r.size();
if(not coprime) {
auto gcd = [&](auto self, Int a, Int b) -> Int {
if(b == 0) return a;
return self(self, b, a % b);
};
for(int i = 0; i < n; i++) {
for(int j = 0; j < i; j++) {
Int g = gcd(gcd, m[i], m[j]);
if((r[i] - r[j]) % g != 0) return {0, 0};
m[i] /= g, m[j] /= g;
Int gi = gcd(gcd, m[i], g), gj = g / gi;
do {
g = gcd(gcd, gi, gj);
gi *= g, gj /= g;
} while(g != 1);
m[i] *= gi, m[j] *= gj;
r[i] %= m[i], r[j] %= m[j];
}
}
}
m.push_back(M);
std::vector<Int> a(n + 1, 1), b(n + 1, 0);
for(int k = 0; k < n; k++) {
Int t = safe_mod((r[k] - b[k]) * mod_inv(a[k], m[k]), m[k]);
for(int i = k + 1; i <= n; i++) {
(b[i] += t * a[i]) %= m[i];
(a[i] *= m[k]) %= m[i];
}
}
return {b[n], a[n]};
}
#line 3 "cp-library/src/utility/random.hpp"
namespace randnum {
static uint seed;
static std::mt19937 mt;
struct gen_seed {
gen_seed() {
seed = std::random_device()();
mt = std::mt19937(seed);
}
} gs;
// [L, R)
template < class T >
T gen_int(T L, T R) {
return std::uniform_int_distribution< T >(L, R - 1)(mt);
}
template < class T >
T get_real(T L, T R) {
return std::uniform_real_distribution< T >(L, R)(mt);
}
}
#line 4 "cp-library/src/number/modfunc.hpp"
u64 modpow64(u64 a, u64 n, u64 mod) {
a %= mod;
u64 res = 1;
while(n > 0) {
if(n % 2 == 1) res = i128(res) * a % mod;
a = i128(a) * a % mod;
n /= 2;
}
return res;
}
u64 modpow(u64 a, u64 n, u64 mod) {
a %= mod;
u64 res = 1;
while(n > 0) {
if(n % 2 == 1) res = res * a % mod;
a = a * a % mod;
n /= 2;
}
return res;
}
long long modinv(long long a, long long m) {
long long b = m, u = 1, v = 0;
while (b) {
long long t = a / b;
a -= t * b; swap(a, b);
u -= t * v; swap(u, v);
}
u %= m;
if (u < 0) u += m;
return u;
}
// solve x^2 = a (mod p)
// return x
// or No Solution (-1)
i32 modsqrt(i32 a, i32 p) {
if(p == 2) return a;
a %= p;
if(a == 0) return 0;
if(modpow(a, (p - 1) / 2, p) != 1) return -1;
i32 q = p - 1, m = 0; while(q % 2 == 0) q /= 2, m++;
i32 z; do { z = randnum::gen_int<i32>(1, p); } while(modpow(z, (p - 1) / 2, p) != p - 1);
i64 c = modpow(z, q, p), t = modpow(a, q, p), r = modpow(a, (q + 1) / 2, p);
while(m > 1) {
if(modpow(t, 1 << (m - 2), p) != 1) r = r * c % p, t = t * (c * c % p) % p;
c = c * c % p;
m -= 1;
}
return r;
}
#line 5 "cp-library/src/number/prime.hpp"
bool miller_rabin(u64 n, std::vector<u64> witness) {
if(n == 1) return false;
if(n % 2 == 0) return n == 2;
u64 d = n - 1;
while(d % 2 == 0) d /= 2;
for(u64 a : witness) if(a < n) {
u64 y = modpow64(a, d, n), t = d;
while(t != n - 1 and y != 1 and y != n - 1) {
y = i128(y) * y % n;
t *= 2;
}
if(y != n - 1 and t % 2 == 0) return false;
}
return true;
}
bool prime_test(u64 n) {
if(n < (u64(1) << 32)) return miller_rabin(n, {2, 7, 61});
return miller_rabin(n, {2, 325, 9375, 28178, 450775, 9780504, 1795265022});
}
u64 pollard_rho(u64 n) {
if(n % 2 == 0) return 2;
if(prime_test(n)) return n;
while(true) {
u64 R = randnum::gen_int<u64>(2, n), x, y = randnum::gen_int<u64>(2, n), ys, q = 1, g = 1, m = 128;
auto f = [&](u64 x) {
return (i128(x) * x % n + R) % n;
};
for(int r = 1; g == 1; r *= 2) {
x = y;
for(int i : rep(r)) y = f(y);
for(int k = 0; g == 1 and k < r; k += m) {
ys = y;
for(int i = 0; i < m and i < r - k; i++) {
q = i128(q) * ((x - (y = f(y)) + n) % n) % n;
}
g = gcd(q, n);
}
}
if(g == n) { do { g = gcd((x - (ys = f(ys))), n); } while(g == 1); }
if(g != n) return g;
}
return 0;
}
std::vector<u64> factor(u64 n) {
function<std::vector<u64>(u64)> dfs = [&](u64 n) {
if(n <= 1) return std::vector<u64>{};
u64 d = pollard_rho(n);
if(d == n) return std::vector<u64>{n};
std::vector<u64> L = dfs(d), R = dfs(n / d);
L.insert(L.end(), R.begin(), R.end());
return L;
};
std::vector<u64> res = dfs(n);
sort(res.begin(), res.end());
return res;
}
std::vector<std::pair<u64, i32>> factor_pair(u64 n) {
std::vector<u64> pf = factor(n);
std::vector<std::pair<u64, i32>> res;
if(pf.empty()) return res;
res.push_back({pf[0], 1});
for(int i : rep(1, int(pf.size()))) {
if(res.back().first == pf[i]) res.back().second++;
else res.push_back({pf[i], 1});
}
return res;
}
u64 euler_phi(u64 n) {
std::vector<std::pair<u64,i32>> pf = factor_pair(n);
for(auto [p, e] : pf) n -= n / p;
return n;
}
#line 5 "A.cpp"
pair<i64, i64> f(i64 s, i64 x) {
assert(x % 2 == 1 or s % 2 == 0);
vector<i64> r, m;
for(auto [p, e] : factor_pair(x)) {
r.push_back(1 + (s % p == 1));
m.push_back(p);
}
auto [a, L] = crt(r, m);
assert(gcd(a, x) == 1 and gcd(s - a, x) == 1);
return make_pair(a, s - a);
}
int main() {
i64 s = in(), x = in();
if(gcd(s, x) == 1) {
print(1);
print(s);
} else {
if(x % 2 == 1 or s % 2 == 0) {
auto [a, b] = f(s, x);
print(2);
print(a, b);
} else {
auto [a, b] = f(s - 1, x);
print(3);
print(1, a, b);
}
}
}
这程序好像有点Bug,我给组数据试试?
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 0ms
memory: 3776kb
input:
9 6
output:
3 1 1 7
result:
ok Correct
Test #2:
score: 0
Accepted
time: 0ms
memory: 3612kb
input:
14 34
output:
2 1 13
result:
ok Correct
Test #3:
score: 0
Accepted
time: 0ms
memory: 3580kb
input:
1000000000 223092870
output:
2 148728581 851271419
result:
ok Correct
Test #4:
score: 0
Accepted
time: 0ms
memory: 3624kb
input:
2 1000000000
output:
2 1 1
result:
ok Correct
Test #5:
score: 0
Accepted
time: 0ms
memory: 3772kb
input:
649557664 933437700
output:
2 83981 649473683
result:
ok Correct
Test #6:
score: 0
Accepted
time: 0ms
memory: 3552kb
input:
33396678 777360870
output:
2 1 33396677
result:
ok Correct
Test #7:
score: 0
Accepted
time: 0ms
memory: 3548kb
input:
48205845 903124530
output:
3 1 18811 48187033
result:
ok Correct
Test #8:
score: 0
Accepted
time: 0ms
memory: 3516kb
input:
251037078 505905400
output:
2 1 251037077
result:
ok Correct
Test #9:
score: 0
Accepted
time: 0ms
memory: 3816kb
input:
30022920 172746860
output:
2 1 30022919
result:
ok Correct
Test #10:
score: 0
Accepted
time: 0ms
memory: 3612kb
input:
63639298 808058790
output:
2 248711 63390587
result:
ok Correct
Test #11:
score: 0
Accepted
time: 0ms
memory: 3556kb
input:
76579017 362768406
output:
3 1 1 76579015
result:
ok Correct
Test #12:
score: 0
Accepted
time: 0ms
memory: 3636kb
input:
40423669 121437778
output:
3 1 1 40423667
result:
ok Correct
Test #13:
score: 0
Accepted
time: 0ms
memory: 3632kb
input:
449277309 720915195
output:
2 1 449277308
result:
ok Correct
Test #14:
score: 0
Accepted
time: 0ms
memory: 3512kb
input:
81665969 919836918
output:
3 1 68069 81597899
result:
ok Correct
Test #15:
score: 0
Accepted
time: 0ms
memory: 3616kb
input:
470578680 280387800
output:
2 1 470578679
result:
ok Correct
Test #16:
score: 0
Accepted
time: 0ms
memory: 3572kb
input:
58450340 803305503
output:
2 1 58450339
result:
ok Correct
Test #17:
score: 0
Accepted
time: 0ms
memory: 3452kb
input:
125896113 323676210
output:
3 1 59281 125836831
result:
ok Correct
Test #18:
score: 0
Accepted
time: 0ms
memory: 3772kb
input:
381905348 434752500
output:
2 1 381905347
result:
ok Correct
Test #19:
score: 0
Accepted
time: 0ms
memory: 3572kb
input:
78916498 653897673
output:
1 78916498
result:
ok Correct
Test #20:
score: 0
Accepted
time: 0ms
memory: 3636kb
input:
35787885 270845190
output:
3 1 1 35787883
result:
ok Correct
Extra Test:
score: 0
Extra Test Passed