結果
| 問題 | No.941 商とあまり |
| ユーザー |
 Pachicobue
|
| 提出日時 | 2019-12-04 20:04:48 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 19,832 bytes |
| コンパイル時間 | 3,265 ms |
| コンパイル使用メモリ | 233,180 KB |
| 実行使用メモリ | 83,512 KB |
| 最終ジャッジ日時 | 2024-05-08 06:47:25 |
| 合計ジャッジ時間 | 10,436 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge2 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | TLE | - |
| testcase_01 | -- | - |
| testcase_02 | -- | - |
| testcase_03 | -- | - |
| testcase_04 | -- | - |
| testcase_05 | -- | - |
| testcase_06 | -- | - |
| testcase_07 | -- | - |
| testcase_08 | -- | - |
| testcase_09 | -- | - |
| testcase_10 | -- | - |
| testcase_11 | -- | - |
| testcase_12 | -- | - |
| testcase_13 | -- | - |
| testcase_14 | -- | - |
| testcase_15 | -- | - |
| testcase_16 | -- | - |
| testcase_17 | -- | - |
| testcase_18 | -- | - |
| testcase_19 | -- | - |
| testcase_20 | -- | - |
| testcase_21 | -- | - |
| testcase_22 | -- | - |
| testcase_23 | -- | - |
| testcase_24 | -- | - |
| testcase_25 | -- | - |
| testcase_26 | -- | - |
| testcase_27 | -- | - |
| testcase_28 | -- | - |
| testcase_29 | -- | - |
| testcase_30 | -- | - |
| testcase_31 | -- | - |
| testcase_32 | -- | - |
| testcase_33 | -- | - |
| testcase_34 | -- | - |
| testcase_35 | -- | - |
| testcase_36 | -- | - |
| testcase_37 | -- | - |
| testcase_38 | -- | - |
| testcase_39 | -- | - |
| testcase_40 | -- | - |
| testcase_41 | -- | - |
| testcase_42 | -- | - |
| testcase_43 | -- | - |
| testcase_44 | -- | - |
| testcase_45 | -- | - |
| testcase_46 | -- | - |
| testcase_47 | -- | - |
| testcase_48 | -- | - |
| testcase_49 | -- | - |
| testcase_50 | -- | - |
| testcase_51 | -- | - |
| testcase_52 | -- | - |
| testcase_53 | -- | - |
| testcase_54 | -- | - |
| testcase_55 | -- | - |
| testcase_56 | -- | - |
| testcase_57 | -- | - |
| testcase_58 | -- | - |
| testcase_59 | -- | - |
| testcase_60 | -- | - |
| testcase_61 | -- | - |
| testcase_62 | -- | - |
| testcase_63 | -- | - |
| testcase_64 | -- | - |
| testcase_65 | -- | - |
| testcase_66 | -- | - |
| testcase_67 | -- | - |
| testcase_68 | -- | - |
| testcase_69 | -- | - |
| testcase_70 | -- | - |
| testcase_71 | -- | - |
| testcase_72 | -- | - |
| testcase_73 | -- | - |
| testcase_74 | -- | - |
| testcase_75 | -- | - |
| testcase_76 | -- | - |
| testcase_77 | -- | - |
| testcase_78 | -- | - |
| testcase_79 | -- | - |
| testcase_80 | -- | - |
| testcase_81 | -- | - |
| testcase_82 | -- | - |
| testcase_83 | -- | - |
| testcase_84 | -- | - |
| testcase_85 | -- | - |
| testcase_86 | -- | - |
| testcase_87 | -- | - |
| testcase_88 | -- | - |
| testcase_89 | -- | - |
| testcase_90 | -- | - |
| testcase_91 | -- | - |
| testcase_92 | -- | - |
| testcase_93 | -- | - |
| testcase_94 | -- | - |
| testcase_95 | -- | - |
| testcase_96 | -- | - |
| testcase_97 | -- | - |
| testcase_98 | -- | - |
| testcase_99 | -- | - |
| testcase_100 | -- | - |
| testcase_101 | -- | - |
| testcase_102 | -- | - |
| testcase_103 | -- | - |
| testcase_104 | -- | - |
| testcase_105 | -- | - |
| testcase_106 | -- | - |
| testcase_107 | -- | - |
| testcase_108 | -- | - |
| testcase_109 | -- | - |
ソースコード
#include <bits/stdc++.h>
// created [2019/12/03] 23:59:35
#pragma GCC diagnostic ignored "-Wsign-compare"
#pragma GCC diagnostic ignored "-Wsign-conversion"
using i32 = int32_t;
using i64 = int64_t;
using u32 = uint32_t;
using u64 = uint64_t;
using uint = unsigned int;
using usize = std::size_t;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
template<typename T> constexpr T popcount(const T u) { return u ? static_cast<T>(__builtin_popcountll(static_cast<u64>(u))) : static_cast<T>(0); }
template<typename T> constexpr T log2p1(const T u) { return u ? static_cast<T>(64 - __builtin_clzll(static_cast<u64>(u))) : static_cast<T>(0); }
template<typename T> constexpr T msbp1(const T u) { return log2p1(u); }
template<typename T> constexpr T lsbp1(const T u) { return __builtin_ffsll(u); }
template<typename T> constexpr T clog(const T u) { return u ? log2p1(u - 1) : static_cast<T>(u); }
template<typename T> constexpr bool ispow2(const T u) { return u and (static_cast<u64>(u) & static_cast<u64>(u - 1)) == 0; }
template<typename T> constexpr T ceil2(const T u) { return static_cast<T>(1) << clog(u); }
template<typename T> constexpr T floor2(const T u) { return u == 0 ? static_cast<T>(0) : static_cast<T>(1) << (log2p1(u) - 1); }
template<typename T> constexpr bool btest(const T mask, const usize ind) { return static_cast<bool>((static_cast<u64>(mask) >> ind) & static_cast<u64>(1)); }
template<typename T> void bset(T& mask, const usize ind) { mask |= (static_cast<T>(1) << ind); }
template<typename T> void breset(T& mask, const usize ind) { mask &= ~(static_cast<T>(1) << ind); }
template<typename T> void bflip(T& mask, const usize ind) { mask ^= (static_cast<T>(1) << ind); }
template<typename T> void bset(T& mask, const usize ind, const bool b) { (b ? bset(mask, ind) : breset(mask, ind)); }
template<typename T> constexpr T bcut(const T mask, const usize ind) { return ind == 0 ? static_cast<T>(0) : static_cast<T>((static_cast<u64>(mask) << (64 - ind)) >> (64 - ind)); }
template<typename T> bool chmin(T& a, const T& b) { return (a > b ? a = b, true : false); }
template<typename T> bool chmax(T& a, const T& b) { return (a < b ? a = b, true : false); }
constexpr unsigned int mod = 1000000007;
template<typename T> constexpr T inf_v = std::numeric_limits<T>::max() / 4;
template<typename Real> constexpr Real pi_v = Real{3.141592653589793238462643383279502884};
template<typename T>
T read()
{
T v;
return std::cin >> v, v;
}
template<typename T, typename... Args>
auto read(const usize size, Args... args)
{
std::vector<decltype(read<T>(args...))> ans(size);
for (usize i = 0; i < size; i++) { ans[i] = read<T>(args...); }
return ans;
}
template<typename... Types>
auto reads() { return std::tuple<std::decay_t<Types>...>{read<Types>()...}; }
# define SHOW(...) static_cast<void>(0)
constexpr ull TEN(const usize n) { return n == 0 ? 1ULL : TEN(n - 1) * 10ULL; }
template<typename T>
std::vector<T> make_v(const usize size, const T v) { return std::vector<T>(size, v); }
template<typename... Args>
auto make_v(const usize size, Args... args) { return std::vector<decltype(make_v(args...))>(size, make_v(args...)); }
template<typename T> T gcd(const T& a, const T& b) { return a < 0 ? gcd(-a, b) : b < 0 ? gcd(a, -b) : (a > b ? gcd(b, a) : a == 0 ? b : gcd(b % a, a)); }
template<typename T> T lcm(const T& a, const T& b) { return a / gcd(a, b) * b; }
template<typename T>
constexpr std::pair<T, T> extgcd(const T a, const T b)
{
if (b == 0) { return std::pair<T, T>{1, 0}; }
const auto g = gcd(a, b), da = std::abs(b) / g;
const auto p = extgcd(b, a % b);
const auto x = (da + p.second % da) % da, y = (g - a * x) / b;
return {x, y};
}
template<typename T>
constexpr T inverse(const T a, const T mod) { return extgcd(a, mod).first; }
template<uint mod_value, bool dynamic = false>
class modint_base
{
public:
template<typename UInt = uint>
static std::enable_if_t<dynamic, const UInt> mod() { return mod_ref(); }
template<typename UInt = uint>
static constexpr std::enable_if_t<not dynamic, const UInt> mod() { return mod_value; }
template<typename UInt = uint>
static void set_mod(const std::enable_if_t<dynamic, const UInt> mod) { mod_ref() = mod, inv_ref() = {1, 1}; }
modint_base() : v{0} {}
modint_base(const ll val) : v{norm(static_cast<uint>(val % static_cast<ll>(mod()) + static_cast<ll>(mod())))} {}
modint_base(const modint_base& n) : v{n()} {}
explicit operator bool() const { return v != 0; }
bool operator!() const { return not static_cast<bool>(*this); }
modint_base& operator=(const modint_base& m) { return v = m(), (*this); }
modint_base& operator=(const ll val) { return v = norm(uint(val % static_cast<ll>(mod()) + static_cast<ll>(mod()))), (*this); }
friend modint_base operator+(const modint_base& m) { return m; }
friend modint_base operator-(const modint_base& m) { return make(norm(mod() - m.v)); }
friend modint_base operator+(const modint_base& m1, const modint_base& m2) { return make(norm(m1.v + m2.v)); }
friend modint_base operator-(const modint_base& m1, const modint_base& m2) { return make(norm(m1.v + mod() - m2.v)); }
friend modint_base operator*(const modint_base& m1, const modint_base& m2) { return make(static_cast<uint>(static_cast<ll>(m1.v) * static_cast<ll>(m2.v) % static_cast<ll>(mod()))); }
friend modint_base operator/(const modint_base& m1, const modint_base& m2) { return m1 * inv(m2.v); }
friend modint_base operator+(const modint_base& m, const ll val) { return modint_base{static_cast<ll>(m.v) + val}; }
friend modint_base operator-(const modint_base& m, const ll val) { return modint_base{static_cast<ll>(m.v) - val}; }
friend modint_base operator*(const modint_base& m, const ll val) { return modint_base{static_cast<ll>(m.v) * (val % static_cast<ll>(mod()))}; }
friend modint_base operator/(const modint_base& m, const ll val) { return modint_base{static_cast<ll>(m.v) * inv(val)}; }
friend modint_base operator+(const ll val, const modint_base& m) { return modint_base{static_cast<ll>(m.v) + val}; }
friend modint_base operator-(const ll val, const modint_base& m) { return modint_base{-static_cast<ll>(m.v) + val}; }
friend modint_base operator*(const ll val, const modint_base& m) { return modint_base{static_cast<ll>(m.v) * (val % static_cast<ll>(mod()))}; }
friend modint_base operator/(const ll val, const modint_base& m) { return modint_base{val * inv(static_cast<ll>(m.v))}; }
friend modint_base& operator+=(modint_base& m1, const modint_base& m2) { return m1 = m1 + m2; }
friend modint_base& operator-=(modint_base& m1, const modint_base& m2) { return m1 = m1 - m2; }
friend modint_base& operator*=(modint_base& m1, const modint_base& m2) { return m1 = m1 * m2; }
friend modint_base& operator/=(modint_base& m1, const modint_base& m2) { return m1 = m1 / m2; }
friend modint_base& operator+=(modint_base& m, const ll val) { return m = m + val; }
friend modint_base& operator-=(modint_base& m, const ll val) { return m = m - val; }
friend modint_base& operator*=(modint_base& m, const ll val) { return m = m * val; }
friend modint_base& operator/=(modint_base& m, const ll val) { return m = m / val; }
friend modint_base operator^(const modint_base& m, const ll n) { return power(m.v, n); }
friend modint_base& operator^=(modint_base& m, const ll n) { return m = m ^ n; }
friend bool operator==(const modint_base& m1, const modint_base& m2) { return m1.v == m2.v; }
friend bool operator!=(const modint_base& m1, const modint_base& m2) { return not(m1 == m2); }
friend bool operator==(const modint_base& m, const ll val) { return m.v == norm(static_cast<uint>(static_cast<ll>(mod()) + val % static_cast<ll>(mod()))); }
friend bool operator!=(const modint_base& m, const ll val) { return not(m == val); }
friend bool operator==(const ll val, const modint_base& m) { return m.v == norm(static_cast<uint>(static_cast<ll>(mod()) + val % static_cast<ll>(mod()))); }
friend bool operator!=(const ll val, const modint_base& m) { return not(m == val); }
friend std::istream& operator>>(std::istream& is, modint_base& m)
{
ll v;
return is >> v, m = v, is;
}
friend std::ostream& operator<<(std::ostream& os, const modint_base& m) { return os << m(); }
uint operator()() const { return v; }
static modint_base small_inv(const usize n)
{
auto& in = inv_ref();
if (n < in.size()) { return in[n]; }
for (usize i = in.size(); i <= n; i++) { in.push_back(-in[modint_base::mod() % i] * (modint_base::mod() / i)); }
return in.back();
}
private:
template<typename UInt = uint>
static std::enable_if_t<dynamic, UInt&> mod_ref()
{
static UInt mod = 0;
return mod;
}
static uint norm(const uint x) { return x < mod() ? x : x - mod(); }
static modint_base make(const uint x)
{
modint_base m;
return m.v = x, m;
}
static modint_base power(modint_base x, ull n)
{
modint_base ans = 1;
for (; n; n >>= 1, x *= x) {
if (n & 1) { ans *= x; }
}
return ans;
}
static modint_base inv(const ll v) { return v < 10000000 ? small_inv(static_cast<usize>(v)) : modint_base{inverse(v, static_cast<ll>(mod()))}; }
// static modint_base inv(const ll v) { return modint_base{inverse(v, static_cast<ll>(mod()))}; }
static std::vector<modint_base>& inv_ref()
{
static std::vector<modint_base> in{1, 1};
return in;
}
uint v;
};
template<uint mod>
using modint = modint_base<mod, false>;
template<uint id>
using dynamic_modint = modint_base<id, true>;
/**
* http://xoshiro.di.unimi.it/xoshiro128starstar.c
* http://xoshiro.di.unimi.it/xoshiro256starstar.c
* http://xoshiro.di.unimi.it/splitmix64.c
*/
class xoshiro
{
public:
using result_type = uint32_t;
static constexpr result_type min() { return std::numeric_limits<result_type>::min(); }
static constexpr result_type max() { return std::numeric_limits<result_type>::max(); }
xoshiro() : xoshiro(std::random_device{}()) {}
xoshiro(uint64_t seed)
{
uint64_t z = 0;
for (int i = 0; i < 4; i++) { z = (seed += 0x9e3779b97f4a7c15), z = (z ^ (z >> 33)) * 0x62A9D9ED799705F5, z = (z ^ (z >> 28)) * 0xCB24D0A5C88C35B3, s[i] = static_cast<result_type>(z >> 32); }
}
result_type operator()()
{
const result_type result = rotl(s[1] * 5, 7) * 9, t = s[1] << 9;
return s[2] ^= s[0], s[3] ^= s[1], s[1] ^= s[2], s[0] ^= s[3], s[2] ^= t, s[3] = rotl(s[3], 11), result;
}
void discard(const usize rep)
{
for (usize i = 0; i < rep; i++) { (*this)(); }
}
private:
result_type s[4];
static result_type rotl(const result_type x, const int k) { return (x << k) | (x >> (32 - k)); }
};
class xoshiro_64
{
public:
using result_type = uint64_t;
static constexpr result_type min() { return std::numeric_limits<result_type>::min(); }
static constexpr result_type max() { return std::numeric_limits<result_type>::max(); }
xoshiro_64() : xoshiro_64(std::random_device{}()) {}
xoshiro_64(uint64_t seed)
{
uint64_t z = 0;
for (int i = 0; i < 4; i++) { z = (seed += 0x9e3779b97f4a7c15), z = (z ^ (z >> 30)) * 0xbf58476d1ce4e5b9, z = (z ^ (z >> 27)) * 0x94d049bb133111eb, s[i] = static_cast<result_type>(z ^ (z >> 31)); }
}
result_type operator()()
{
const result_type result = rotl(s[1] * 5, 7) * 9, t = s[1] << 17;
return s[2] ^= s[0], s[3] ^= s[1], s[1] ^= s[2], s[0] ^= s[3], s[2] ^= t, s[3] = rotl(s[3], 45), result;
}
void discard(const usize rep)
{
for (usize i = 0; i < rep; i++) { (*this)(); }
}
private:
result_type s[4];
static result_type rotl(const result_type x, const int k) { return (x << k) | (x >> (64 - k)); }
};
template<typename Rng>
class rng_base
{
public:
using rng_type = Rng;
using result_type = typename rng_type::result_type;
static constexpr result_type min() { return rng_type::min(); }
static constexpr result_type max() { return rng_type::max(); }
rng_base() : rng_base(std::random_device{}()) {}
rng_base(const u64 seed) : rng(seed) {}
~rng_base() = default;
result_type operator()(const result_type max = std::numeric_limits<result_type>::max())
{
if (max == std::numeric_limits<result_type>::max()) { return static_cast<result_type>(rng()); }
if (ispow2(max + 1)) { return static_cast<result_type>(rng() & max); }
const result_type mask = static_cast<result_type>(ceil2(static_cast<u64>(max + 1))) - 1;
while (true) {
const result_type ans = static_cast<result_type>(rng() & mask);
if (ans <= max) { return ans; }
}
}
result_type operator()(const result_type min, const result_type max) { return min + (*this)(max - min); }
operator bool() { return *this(0, 1); }
template<typename Int> std::pair<Int, Int> pair(const Int min, const Int max, const bool sorted = false) { return sorted ? std::minmax(*this(min, max), *this(min, max)) : std::pair<Int, Int>{*this(min, max), *this(min, max)}; }
template<typename Int>
std::vector<Int> vec(const std::size_t size, const Int min, const Int max)
{
std::vector<Int> v(size);
for (std::size_t i = 0; i < size; i++) { v[i] = *this(min, max); }
return v;
}
std::vector<usize> perm(const usize n)
{
std::vector<usize> ans(n);
std::iota(ans.begin(), ans.end(), 0UL);
std::shuffle(ans.begin(), ans.end(), rng);
return ans;
}
private:
Rng rng;
};
using rng_mt = rng_base<std::mt19937>;
using rng_mt64 = rng_base<std::mt19937_64>;
using rng_xoshiro = rng_base<xoshiro>;
using rng_xoshiro64 = rng_base<xoshiro_64>;
rng_mt g_rng_mt;
rng_mt64 g_rng_mt64;
rng_xoshiro g_rng_xo;
rng_xoshiro64 g_rng_xo64;
int main()
{
std::cin.tie(nullptr), std::ios::sync_with_stdio(false);
const int N = read<int>();
const ull X = read<ull>();
auto A = read<ull>(N);
std::sort(A.begin(), A.end());
{
ull x = X + 1;
for (const ull a : A) { x /= (a + 1); }
if (x == 0) { return std::cout << std::string(X, '0') << std::endl, 0; }
}
ull p = 1;
for (const ull a : A) { p *= (a + 1); }
p--;
{
if (N == 1) {
std::string ans(X, '0');
ans[A[0] - 1] = '1';
return std::cout << ans << std::endl, 0;
}
}
{
if (N == 2) {
for (ull i = 1; i <= X; i++) {
if (i < p) {
std::cout << 0;
} else {
const ull y = i - p;
std::cout << (y % A[0] == 0 or y % A[1] == 0);
}
}
std::cout << std::endl;
return 0;
}
}
{
std::set<ull> kind;
for (const ull a : A) { kind.insert(a); }
if (kind.size() == 1) {
const ull x = *kind.begin();
std::vector<bool> ok(X + 1, false);
for (ull q = p; q <= X; q += x) {
ok[q] = true;
}
for (int i = 1; i <= X; i++) {
std::cout << (ok[i]);
}
std::cout << std::endl;
return 0;
}
}
ull g = 0;
for (const ull a : A) { g = std::gcd(g, a); }
{
if (A[0] == g) {
for (int i = 1; i <= X; i++) {
if (i >= p) {
const ull d = i - p;
std::cout << (d % g == 0);
} else {
std::cout << 0;
}
}
std::cout << std::endl;
return 0;
}
}
constexpr uint mod = 9999991; // ひえ〜
using mint = modint<mod>;
std::vector<mint> hs(X + 1), ihs(X + 1, 1);
for (int i = 0; i <= X; i++) { hs[i] = g_rng_xo(2, mod - 2), ihs[i] /= hs[i]; }
constexpr ull NONE = 1ULL << 60;
std::vector<ull> v = A;
mint hash = 1;
for (const ull a : A) { hash *= hs[a]; }
ull product = 1;
for (const ull a : A) { product *= (a + 1); }
ull max = X;
for (int i = 0; i < N; i++) {
for (int j = i + 1; j < N; j++) {
chmax(max, (A[i] + 1) * (A[j] + 1));
}
}
const ull L = std::min(X, p + max * 2); // 根拠は無いですごめんなさい
// const ull L = X;
std::vector<int> is(N);
auto inds_of = [&](const std::vector<ull>& v) {
std::vector<int> ans;
for (int i = 0; i < N; i++) {
if (v[i] == NONE) { continue; }
ans.push_back(i);
}
return ans;
};
std::vector<bool> ok(X + 1, false);
auto in = [&](const int i, const int j, const ull x, const ull y, const ull z) {
v[i] = z, v[j] = NONE;
((product /= (x + 1)) /= (y + 1)) *= (z + 1);
((hash *= ihs[x]) *= ihs[y]) *= hs[z];
};
auto out = [&](const int i, const int j, const ull x, const ull y, const ull z) {
v[i] = x, v[j] = y;
((product *= (x + 1)) *= (y + 1)) /= (z + 1);
((hash *= hs[x]) *= hs[y]) *= ihs[z];
};
std::set<uint> used_hash;
used_hash.insert(hash());
auto dfs = [&](auto&& self) -> void {
const auto is = inds_of(v);
const int size = is.size();
if (size == 2) {
const ull x = v[is[0]], y = v[is[1]];
const ull new_value = (x + 1) * (y + 1) - 1;
for (ull z = new_value;; z += x) {
if (z > L) { break; }
ok[z] = true;
}
for (ull z = new_value + y;; z += y) {
if (z > L) { break; }
ok[z] = true;
}
return;
}
std::set<uint> used_new_hash;
for (int i_ = 0; i_ < size; i_++) {
for (int j_ = i_ + 1; j_ < size; j_++) {
const int i = is[i_], j = is[j_];
const ull x = v[i], y = v[j];
const mint new_hash = hash * ihs[x] * ihs[y];
if (used_new_hash.find(new_hash()) != used_new_hash.end()) { continue; }
used_new_hash.insert(new_hash());
const ull new_product = product / (x + 1) / (y + 1);
const ull new_value = (x + 1) * (y + 1) - 1;
for (ull z = new_value;; z += x) {
ull next_product = new_product * (z + 1);
if (next_product > L + 1) { break; }
mint next_hash = new_hash * hs[z];
if (used_hash.find(next_hash()) != used_hash.end()) { continue; }
used_hash.insert(next_hash());
in(i, j, x, y, z);
self(self);
out(i, j, x, y, z);
}
for (ull z = new_value + y;; z += y) {
ull next_product = new_product * (z + 1);
if (next_product > L + 1) { break; }
mint next_hash = new_hash * hs[z];
if (used_hash.find(next_hash()) != used_hash.end()) { continue; }
used_hash.insert(next_hash());
in(i, j, x, y, z);
self(self);
out(i, j, x, y, z);
}
}
}
};
dfs(dfs);
std::cerr << used_hash.size() << std::endl;
for (int x = 1; x <= X; x++) {
if (x <= L) {
std::cout << ok[x];
} else {
std::cout << ((x - p) % g == 0);
}
}
std::cout << std::endl;
return 0;
}