結果
| 問題 | No.2479 Sum of Squares |
| ユーザー |
 maspy
|
| 提出日時 | 2023-10-25 08:10:39 |
| 言語 | C++23 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 2 ms / 2,000 ms |
| コード長 | 29,710 bytes |
| コンパイル時間 | 5,289 ms |
| コンパイル使用メモリ | 301,184 KB |
| 実行使用メモリ | 4,348 KB |
| 最終ジャッジ日時 | 2023-10-25 08:10:46 |
| 合計ジャッジ時間 | 6,453 ms |
|
ジャッジサーバーID （参考情報） |
judge15 / judge12 |
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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 | AC | 2 ms
4,348 KB |
| testcase_01 | AC | 2 ms
4,348 KB |
| testcase_02 | AC | 2 ms
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| testcase_03 | AC | 2 ms
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| testcase_04 | AC | 2 ms
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| testcase_05 | AC | 2 ms
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| testcase_06 | AC | 2 ms
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| testcase_07 | AC | 2 ms
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| testcase_08 | AC | 2 ms
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| testcase_09 | AC | 2 ms
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| testcase_10 | AC | 2 ms
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| testcase_11 | AC | 2 ms
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| testcase_12 | AC | 2 ms
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| testcase_13 | AC | 2 ms
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| testcase_14 | AC | 2 ms
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| testcase_15 | AC | 2 ms
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| testcase_16 | AC | 2 ms
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| testcase_17 | AC | 2 ms
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| testcase_18 | AC | 2 ms
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| testcase_19 | AC | 2 ms
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| testcase_20 | AC | 2 ms
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| testcase_21 | AC | 2 ms
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| testcase_22 | AC | 2 ms
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| testcase_23 | AC | 2 ms
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| testcase_24 | AC | 2 ms
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ソースコード
#line 1 "/home/maspy/compro/library/my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;
template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'000'000'000;
template <>
constexpr ll infty<ll> = ll(infty<int>) * infty<int> * 2;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * infty<ll>;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;
using pi = pair<ll, ll>;
using vi = vector<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;
#define vv(type, name, h, ...) \
vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...) \
vector<vector<vector<type>>> name( \
h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...) \
vector<vector<vector<vector<type>>>> name( \
a, vector<vector<vector<type>>>( \
b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))
// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)
#define FOR_subset(t, s) \
for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if
#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second
#define stoi stoll
int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
int popcnt_mod_2(int x) { return __builtin_parity(x); }
int popcnt_mod_2(u32 x) { return __builtin_parity(x); }
int popcnt_mod_2(ll x) { return __builtin_parityll(x); }
int popcnt_mod_2(u64 x) { return __builtin_parityll(x); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
template <typename T, typename U>
T ceil(T x, U y) {
return (x > 0 ? (x + y - 1) / y : x / y);
}
template <typename T, typename U>
T floor(T x, U y) {
return (x > 0 ? x / y : (x - y + 1) / y);
}
template <typename T, typename U>
T bmod(T x, U y) {
return x - y * floor(x, y);
}
template <typename T, typename U>
pair<T, T> divmod(T x, U y) {
T q = floor(x, y);
return {q, x - q * y};
}
template <typename T, typename U>
T SUM(const vector<U> &A) {
T sum = 0;
for (auto &&a: A) sum += a;
return sum;
}
#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) \
sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()
template <typename T>
T POP(deque<T> &que) {
T a = que.front();
que.pop_front();
return a;
}
template <typename T>
T POP(pq<T> &que) {
T a = que.top();
que.pop();
return a;
}
template <typename T>
T POP(pqg<T> &que) {
T a = que.top();
que.pop();
return a;
}
template <typename T>
T POP(vc<T> &que) {
T a = que.back();
que.pop_back();
return a;
}
template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
if (check_ok) assert(check(ok));
while (abs(ok - ng) > 1) {
auto x = (ng + ok) / 2;
(check(x) ? ok : ng) = x;
}
return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
FOR(iter) {
double x = (ok + ng) / 2;
(check(x) ? ok : ng) = x;
}
return (ok + ng) / 2;
}
template <class T, class S>
inline bool chmax(T &a, const S &b) {
return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
return (a > b ? a = b, 1 : 0);
}
// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
vc<int> A(S.size());
FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
return A;
}
template <typename T, typename U>
vector<T> cumsum(vector<U> &A, int off = 1) {
int N = A.size();
vector<T> B(N + 1);
FOR(i, N) { B[i + 1] = B[i] + A[i]; }
if (off == 0) B.erase(B.begin());
return B;
}
// stable sort
template <typename T>
vector<int> argsort(const vector<T> &A) {
vector<int> ids(len(A));
iota(all(ids), 0);
sort(all(ids),
[&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
return ids;
}
// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
vc<T> B(len(I));
FOR(i, len(I)) B[i] = A[I[i]];
return B;
}
#endif
#line 1 "/home/maspy/compro/library/other/io.hpp"
// based on yosupo's fastio
#include <unistd.h>
namespace fastio {
#define FASTIO
// クラスが read(), print() を持っているかを判定するメタ関数
struct has_write_impl {
template <class T>
static auto check(T &&x) -> decltype(x.write(), std::true_type{});
template <class T>
static auto check(...) -> std::false_type;
};
template <class T>
class has_write : public decltype(has_write_impl::check<T>(std::declval<T>())) {
};
struct has_read_impl {
template <class T>
static auto check(T &&x) -> decltype(x.read(), std::true_type{});
template <class T>
static auto check(...) -> std::false_type;
};
template <class T>
class has_read : public decltype(has_read_impl::check<T>(std::declval<T>())) {};
struct Scanner {
FILE *fp;
char line[(1 << 15) + 1];
size_t st = 0, ed = 0;
void reread() {
memmove(line, line + st, ed - st);
ed -= st;
st = 0;
ed += fread(line + ed, 1, (1 << 15) - ed, fp);
line[ed] = '\0';
}
bool succ() {
while (true) {
if (st == ed) {
reread();
if (st == ed) return false;
}
while (st != ed && isspace(line[st])) st++;
if (st != ed) break;
}
if (ed - st <= 50) {
bool sep = false;
for (size_t i = st; i < ed; i++) {
if (isspace(line[i])) {
sep = true;
break;
}
}
if (!sep) reread();
}
return true;
}
template <class T, enable_if_t<is_same<T, string>::value, int> = 0>
bool read_single(T &ref) {
if (!succ()) return false;
while (true) {
size_t sz = 0;
while (st + sz < ed && !isspace(line[st + sz])) sz++;
ref.append(line + st, sz);
st += sz;
if (!sz || st != ed) break;
reread();
}
return true;
}
template <class T, enable_if_t<is_integral<T>::value, int> = 0>
bool read_single(T &ref) {
if (!succ()) return false;
bool neg = false;
if (line[st] == '-') {
neg = true;
st++;
}
ref = T(0);
while (isdigit(line[st])) { ref = 10 * ref + (line[st++] & 0xf); }
if (neg) ref = -ref;
return true;
}
template <typename T,
typename enable_if<has_read<T>::value>::type * = nullptr>
inline bool read_single(T &x) {
x.read();
return true;
}
bool read_single(double &ref) {
string s;
if (!read_single(s)) return false;
ref = std::stod(s);
return true;
}
bool read_single(char &ref) {
string s;
if (!read_single(s) || s.size() != 1) return false;
ref = s[0];
return true;
}
template <class T>
bool read_single(vector<T> &ref) {
for (auto &d: ref) {
if (!read_single(d)) return false;
}
return true;
}
template <class T, class U>
bool read_single(pair<T, U> &p) {
return (read_single(p.first) && read_single(p.second));
}
template <size_t N = 0, typename T>
void read_single_tuple(T &t) {
if constexpr (N < std::tuple_size<T>::value) {
auto &x = std::get<N>(t);
read_single(x);
read_single_tuple<N + 1>(t);
}
}
template <class... T>
bool read_single(tuple<T...> &tpl) {
read_single_tuple(tpl);
return true;
}
void read() {}
template <class H, class... T>
void read(H &h, T &... t) {
bool f = read_single(h);
assert(f);
read(t...);
}
Scanner(FILE *fp) : fp(fp) {}
};
struct Printer {
Printer(FILE *_fp) : fp(_fp) {}
~Printer() { flush(); }
static constexpr size_t SIZE = 1 << 15;
FILE *fp;
char line[SIZE], small[50];
size_t pos = 0;
void flush() {
fwrite(line, 1, pos, fp);
pos = 0;
}
void write(const char val) {
if (pos == SIZE) flush();
line[pos++] = val;
}
template <class T, enable_if_t<is_integral<T>::value, int> = 0>
void write(T val) {
if (pos > (1 << 15) - 50) flush();
if (val == 0) {
write('0');
return;
}
if (val < 0) {
write('-');
val = -val; // todo min
}
size_t len = 0;
while (val) {
small[len++] = char(0x30 | (val % 10));
val /= 10;
}
for (size_t i = 0; i < len; i++) { line[pos + i] = small[len - 1 - i]; }
pos += len;
}
void write(const string s) {
for (char c: s) write(c);
}
void write(const char *s) {
size_t len = strlen(s);
for (size_t i = 0; i < len; i++) write(s[i]);
}
void write(const double x) {
ostringstream oss;
oss << fixed << setprecision(15) << x;
string s = oss.str();
write(s);
}
void write(const long double x) {
ostringstream oss;
oss << fixed << setprecision(15) << x;
string s = oss.str();
write(s);
}
template <typename T,
typename enable_if<has_write<T>::value>::type * = nullptr>
inline void write(T x) {
x.write();
}
template <class T>
void write(const vector<T> val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) write(' ');
write(val[i]);
}
}
template <class T, class U>
void write(const pair<T, U> val) {
write(val.first);
write(' ');
write(val.second);
}
template <size_t N = 0, typename T>
void write_tuple(const T t) {
if constexpr (N < std::tuple_size<T>::value) {
if constexpr (N > 0) { write(' '); }
const auto x = std::get<N>(t);
write(x);
write_tuple<N + 1>(t);
}
}
template <class... T>
bool write(tuple<T...> tpl) {
write_tuple(tpl);
return true;
}
template <class T, size_t S>
void write(const array<T, S> val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) write(' ');
write(val[i]);
}
}
void write(i128 val) {
string s;
bool negative = 0;
if (val < 0) {
negative = 1;
val = -val;
}
while (val) {
s += '0' + int(val % 10);
val /= 10;
}
if (negative) s += "-";
reverse(all(s));
if (len(s) == 0) s = "0";
write(s);
}
};
Scanner scanner = Scanner(stdin);
Printer printer = Printer(stdout);
void flush() { printer.flush(); }
void print() { printer.write('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
printer.write(head);
if (sizeof...(Tail)) printer.write(' ');
print(forward<Tail>(tail)...);
}
void read() {}
template <class Head, class... Tail>
void read(Head &head, Tail &... tail) {
scanner.read(head);
read(tail...);
}
} // namespace fastio
using fastio::print;
using fastio::flush;
using fastio::read;
#define INT(...) \
int __VA_ARGS__; \
read(__VA_ARGS__)
#define LL(...) \
ll __VA_ARGS__; \
read(__VA_ARGS__)
#define STR(...) \
string __VA_ARGS__; \
read(__VA_ARGS__)
#define CHAR(...) \
char __VA_ARGS__; \
read(__VA_ARGS__)
#define DBL(...) \
double __VA_ARGS__; \
read(__VA_ARGS__)
#define VEC(type, name, size) \
vector<type> name(size); \
read(name)
#define VV(type, name, h, w) \
vector<vector<type>> name(h, vector<type>(w)); \
read(name)
void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
#line 3 "main.cpp"
#line 2 "/home/maspy/compro/library/mod/dynamic_modint_64.hpp"
#line 2 "/home/maspy/compro/library/mod/modint_common.hpp"
struct has_mod_impl {
template <class T>
static auto check(T &&x) -> decltype(x.get_mod(), std::true_type{});
template <class T>
static auto check(...) -> std::false_type;
};
template <class T>
class has_mod : public decltype(has_mod_impl::check<T>(std::declval<T>())) {};
template <typename mint>
mint inv(int n) {
static const int mod = mint::get_mod();
static vector<mint> dat = {0, 1};
assert(0 <= n);
if (n >= mod) n %= mod;
while (len(dat) <= n) {
int k = len(dat);
int q = (mod + k - 1) / k;
dat.eb(dat[k * q - mod] * mint::raw(q));
}
return dat[n];
}
template <typename mint>
mint fact(int n) {
static const int mod = mint::get_mod();
assert(0 <= n && n < mod);
static vector<mint> dat = {1, 1};
while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * mint::raw(len(dat)));
return dat[n];
}
template <typename mint>
mint fact_inv(int n) {
static vector<mint> dat = {1, 1};
if (n < 0) return mint(0);
while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * inv<mint>(len(dat)));
return dat[n];
}
template <class mint, class... Ts>
mint fact_invs(Ts... xs) {
return (mint(1) * ... * fact_inv<mint>(xs));
}
template <typename mint, class Head, class... Tail>
mint multinomial(Head &&head, Tail &&... tail) {
return fact<mint>(head) * fact_invs<mint>(std::forward<Tail>(tail)...);
}
template <typename mint>
mint C_dense(int n, int k) {
static vvc<mint> C;
static int H = 0, W = 0;
auto calc = [&](int i, int j) -> mint {
if (i == 0) return (j == 0 ? mint(1) : mint(0));
return C[i - 1][j] + (j ? C[i - 1][j - 1] : 0);
};
if (W <= k) {
FOR(i, H) {
C[i].resize(k + 1);
FOR(j, W, k + 1) { C[i][j] = calc(i, j); }
}
W = k + 1;
}
if (H <= n) {
C.resize(n + 1);
FOR(i, H, n + 1) {
C[i].resize(W);
FOR(j, W) { C[i][j] = calc(i, j); }
}
H = n + 1;
}
return C[n][k];
}
template <typename mint, bool large = false, bool dense = false>
mint C(ll n, ll k) {
assert(n >= 0);
if (k < 0 || n < k) return 0;
if constexpr (dense) return C_dense<mint>(n, k);
if constexpr (!large) return multinomial<mint>(n, k, n - k);
k = min(k, n - k);
mint x(1);
FOR(i, k) x *= mint(n - i);
return x * fact_inv<mint>(k);
}
template <typename mint, bool large = false>
mint C_inv(ll n, ll k) {
assert(n >= 0);
assert(0 <= k && k <= n);
if (!large) return fact_inv<mint>(n) * fact<mint>(k) * fact<mint>(n - k);
return mint(1) / C<mint, 1>(n, k);
}
// [x^d] (1-x) ^ {-n} の計算
template <typename mint, bool large = false, bool dense = false>
mint C_negative(ll n, ll d) {
assert(n >= 0);
if (d < 0) return mint(0);
if (n == 0) { return (d == 0 ? mint(1) : mint(0)); }
return C<mint, large, dense>(n + d - 1, d);
}
#line 2 "/home/maspy/compro/library/mod/barrett.hpp"
// https://github.com/atcoder/ac-library/blob/master/atcoder/internal_math.hpp
struct Barrett {
u32 m;
u64 im;
explicit Barrett(u32 m = 1) : m(m), im(u64(-1) / m + 1) {}
u32 umod() const { return m; }
u32 modulo(u64 z) {
if (m == 1) return 0;
u64 x = (u64)(((unsigned __int128)(z)*im) >> 64);
u64 y = x * m;
return (z - y + (z < y ? m : 0));
}
u64 floor(u64 z) {
if (m == 1) return z;
u64 x = (u64)(((unsigned __int128)(z)*im) >> 64);
u64 y = x * m;
return (z < y ? x - 1 : x);
}
pair<u64, u32> divmod(u64 z) {
if (m == 1) return {z, 0};
u64 x = (u64)(((unsigned __int128)(z)*im) >> 64);
u64 y = x * m;
if (z < y) return {x - 1, z - y + m};
return {x, z - y};
}
u32 mul(u32 a, u32 b) { return modulo(u64(a) * b); }
};
struct Barrett_64 {
u128 mod, mh, ml;
explicit Barrett_64(u64 mod = 1) : mod(mod) {
u128 m = u128(-1) / mod;
if (m * mod + mod == u128(0)) ++m;
mh = m >> 64;
ml = m & u64(-1);
}
u64 umod() const { return mod; }
u64 modulo(u128 x) {
u128 z = (x & u64(-1)) * ml;
z = (x & u64(-1)) * mh + (x >> 64) * ml + (z >> 64);
z = (x >> 64) * mh + (z >> 64);
x -= z * mod;
return x < mod ? x : x - mod;
}
u64 mul(u64 a, u64 b) { return modulo(u128(a) * b); }
};
#line 5 "/home/maspy/compro/library/mod/dynamic_modint_64.hpp"
// https://codeforces.com/contest/453/problem/D
template <int id>
struct Dynamic_Modint_64 {
static constexpr bool is_modint = true;
using mint = Dynamic_Modint_64;
u64 val;
static Barrett_64 bt;
static u64 umod() { return bt.umod(); }
static ll get_mod() { return (ll)(bt.umod()); }
static void set_mod(ll m) {
assert(1 <= m);
bt = Barrett_64(m);
}
Dynamic_Modint_64() : val(0) {}
Dynamic_Modint_64(u64 x) : val(bt.modulo(x)) {}
Dynamic_Modint_64(u128 x) : val(bt.modulo(x)) {}
Dynamic_Modint_64(int x) : val((x %= get_mod()) < 0 ? x + get_mod() : x) {}
Dynamic_Modint_64(ll x) : val((x %= get_mod()) < 0 ? x + get_mod() : x) {}
Dynamic_Modint_64(i128 x) : val((x %= get_mod()) < 0 ? x + get_mod() : x) {}
mint& operator+=(const mint& rhs) {
val = (val += rhs.val) < umod() ? val : val - umod();
return *this;
}
mint& operator-=(const mint& rhs) {
val = (val += umod() - rhs.val) < umod() ? val : val - umod();
return *this;
}
mint& operator*=(const mint& rhs) {
val = bt.mul(val, rhs.val);
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inverse(); }
mint operator-() const { return mint() - *this; }
mint pow(ll n) const {
assert(0 <= n);
mint x = *this, r = u64(1);
while (n) {
if (n & 1) r *= x;
x *= x, n >>= 1;
}
return r;
}
mint inverse() const {
ll x = val, mod = get_mod();
ll a = x, b = mod, u = 1, v = 0, t;
while (b > 0) {
t = a / b;
swap(a -= t * b, b), swap(u -= t * v, v);
}
if (u < 0) u += mod;
return u64(u);
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs.val == rhs.val;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs.val != rhs.val;
}
#ifdef FASTIO
void write() { fastio::printer.write(val); }
void read() {
fastio::scanner.read(val);
val = bt.modulo(val);
}
#endif
};
using dmint64 = Dynamic_Modint_64<-1>;
template <int id>
Barrett_64 Dynamic_Modint_64<id>::bt;
#line 3 "/home/maspy/compro/library/nt/primetest.hpp"
bool primetest(const u64 x) {
if (x == 2 or x == 3 or x == 5 or x == 7) return true;
if (x % 2 == 0 or x % 3 == 0 or x % 5 == 0 or x % 7 == 0) return false;
if (x < 121) return x > 1;
const u64 d = (x - 1) >> lowbit(x - 1);
using m64 = Dynamic_Modint_64<20231024>;
m64::set_mod(x);
const m64 one(u64(1)), minus_one(x - 1);
auto ok = [&](u64 a) -> bool {
auto y = m64(a).pow(d);
u64 t = d;
while (y != one && y != minus_one && t != x - 1) y *= y, t <<= 1;
if (y != minus_one && t % 2 == 0) return false;
return true;
};
if (x < (1ull << 32)) {
for (u64 a: {2, 7, 61})
if (!ok(a)) return false;
} else {
for (u64 a: {2, 325, 9375, 28178, 450775, 9780504, 1795265022}) {
if (x <= a) return true;
if (!ok(a)) return false;
}
}
return true;
}
#line 2 "/home/maspy/compro/library/nt/factor.hpp"
#line 2 "/home/maspy/compro/library/random/base.hpp"
u64 RNG_64() {
static uint64_t x_
= uint64_t(chrono::duration_cast<chrono::nanoseconds>(
chrono::high_resolution_clock::now().time_since_epoch())
.count())
* 10150724397891781847ULL;
x_ ^= x_ << 7;
return x_ ^= x_ >> 9;
}
u64 RNG(u64 lim) { return RNG_64() % lim; }
ll RNG(ll l, ll r) { return l + RNG_64() % (r - l); }
#line 5 "/home/maspy/compro/library/nt/factor.hpp"
ll rho(ll n, ll c) {
using m64 = Dynamic_Modint_64<20231025>;
m64::set_mod(n);
assert(n > 1);
const m64 cc(c);
auto f = [&](m64 x) { return x * x + cc; };
m64 x = 1, y = 2, z = 1, q = 1;
ll g = 1;
const ll m = 1LL << (__lg(n) / 5); // ?
for (ll r = 1; g == 1; r <<= 1) {
x = y;
FOR(_, r) y = f(y);
for (ll k = 0; k < r && g == 1; k += m) {
z = y;
FOR(min(m, r - k)) y = f(y), q *= x - y;
g = gcd(q.val, n);
}
}
if (g == n) do {
z = f(z);
g = gcd((x - z).val, n);
} while (g == 1);
return g;
}
ll find_prime_factor(ll n) {
assert(n > 1);
if (primetest(n)) return n;
FOR(100) {
ll m = rho(n, RNG(0, n));
if (primetest(m)) return m;
n = m;
}
assert(0);
return -1;
}
// ソートしてくれる
vc<pair<ll, int>> factor(ll n) {
assert(n >= 1);
vc<pair<ll, int>> pf;
FOR(p, 2, 100) {
if (p * p > n) break;
if (n % p == 0) {
ll e = 0;
do { n /= p, e += 1; } while (n % p == 0);
pf.eb(p, e);
}
}
while (n > 1) {
ll p = find_prime_factor(n);
ll e = 0;
do { n /= p, e += 1; } while (n % p == 0);
pf.eb(p, e);
}
sort(all(pf));
return pf;
}
vc<pair<ll, int>> factor_by_lpf(ll n, vc<int>& lpf) {
vc<pair<ll, int>> res;
while (n > 1) {
int p = lpf[n];
int e = 0;
while (n % p == 0) {
n /= p;
++e;
}
res.eb(p, e);
}
return res;
}
#line 3 "/home/maspy/compro/library/mod/mod_pow.hpp"
int mod_pow(int a, ll n, int mod) {
assert(n >= 0);
a = ((a %= mod) < 0 ? a + mod : a);
Barrett bt(mod);
int p = a, v = bt.modulo(1);
while (n) {
if (n & 1) v = bt.mul(v, p);
p = bt.mul(p, p);
n >>= 1;
}
return v;
}
ll mod_pow_64(ll a, ll n, ll mod) {
assert(n >= 0);
a = ((a %= mod) < 0 ? a + mod : a);
Barrett_64 bt(mod);
ll p = a, v = bt.modulo(1);
while (n) {
if (n & 1) v = bt.mul(v, p);
p = bt.mul(p, p);
n >>= 1;
}
return v;
}
#line 3 "/home/maspy/compro/library/nt/gaussian_integers.hpp"
template <typename T>
struct Gaussian_Integer {
T x, y;
using G = Gaussian_Integer;
Gaussian_Integer(T x = 0, T y = 0) : x(x), y(y) {}
Gaussian_Integer(pair<T, T> p) : x(p.fi), y(p.se) {}
T norm() const { return x * x + y * y; }
G conjugate() const { return G(x, -y); }
G &operator+=(const G &g) {
x += g.x, y += g.y;
return *this;
}
G &operator-=(const G &g) {
x -= g.x, y -= g.y;
return *this;
}
G &operator*=(const G &g) {
tie(x, y) = mp(x * g.x - y * g.y, x * g.y + y * g.x);
return *this;
}
G &operator/=(const G &g) {
*this *= g.conjugate();
T n = g.norm();
x = floor(x + n / 2, n);
y = floor(y + n / 2, n);
return *this;
}
G &operator%=(const G &g) {
auto q = G(*this) / g;
q *= g;
(*this) -= q;
return *this;
}
G operator-() { return G(-x, -y); }
G operator+(const G &g) { return G(*this) += g; }
G operator-(const G &g) { return G(*this) -= g; }
G operator*(const G &g) { return G(*this) *= g; }
G operator/(const G &g) { return G(*this) /= g; }
G operator%(const G &g) { return G(*this) %= g; }
bool operator==(const G &g) { return (x == g.x && y == g.y); }
static G gcd(G a, G b) {
while (b.x != 0 || b.y != 0) {
a %= b;
swap(a, b);
}
return a;
}
// (g,x,y) s.t ax+by=g
static tuple<G, G, G> extgcd(G a, G b) {
if (b.x != 0 || b.y != 0) {
G q = a / b;
auto [g, x, y] = extgcd(b, a - q * b);
return {g, y, x - q * y};
}
return {a, G{1, 0}, G{0, 0}};
}
};
pair<ll, ll> solve_norm_equation_prime(ll p) {
using G = Gaussian_Integer<i128>;
assert(p == 2 || p % 4 == 1);
if (p == 2) return {1, 1};
ll x = [&]() -> ll {
ll x = 1;
while (1) {
++x;
ll pow_x = 1;
if (p < (1 << 30)) {
pow_x = mod_pow(x, (p - 1) / 4, p);
if (pow_x * pow_x % p == p - 1) return pow_x;
} else {
pow_x = mod_pow_64(x, (p - 1) / 4, p);
if (i128(pow_x) * pow_x % p == p - 1) return pow_x;
}
}
return -1;
}();
G a(p, 0), b(x, 1);
a = G::gcd(a, b);
assert(a.norm() == p);
return {a.x, a.y};
}
template <typename T>
vc<Gaussian_Integer<T>> solve_norm_equation_factor(vc<pair<ll, int>> pfs) {
using G = Gaussian_Integer<T>;
vc<G> res;
for (auto &&[p, e]: pfs) {
if (p % 4 == 3 && e % 2 == 1) return {};
}
res.eb(G(1, 0));
for (auto &&[p, e]: pfs) {
if (p % 4 == 3) {
T pp = 1;
FOR(e / 2) pp *= p;
for (auto &&g: res) {
g.x *= pp;
g.y *= pp;
}
continue;
}
G pi = solve_norm_equation_prime(p);
vc<G> pows(e + 1);
pows[0] = G(1, 0);
FOR(i, e) pows[i + 1] = pows[i] * pi;
if (p == 2) {
for (auto &&g: res) g *= pows[e];
continue;
}
vc<G> pis(e + 1);
FOR(j, e + 1) { pis[j] = pows[j] * (pows[e - j].conjugate()); }
vc<G> new_res;
new_res.reserve(len(res) * (e + 1));
for (auto &&g: res) {
for (auto &&a: pis) { new_res.eb(g * a); }
}
swap(res, new_res);
}
for (auto &&g: res) {
while (g.x <= 0 || g.y < 0) { g = G(-g.y, g.x); }
}
return res;
}
// i128 を使うと N <= 10^{18} もできる
// ノルムがとれるように、2 乗してもオーバーフローしない型を使おう
// 0 <= arg < 90 となるもののみ返す。
// 単数倍は作らないので、使うときに気を付ける。
template <typename T>
vc<Gaussian_Integer<T>> solve_norm_equation(T N) {
using G = Gaussian_Integer<T>;
vc<G> res;
if (N < 0) return {};
if (N == 0) {
res.eb(G(0, 0));
return res;
}
auto pfs = factor(N);
return solve_norm_equation_factor<T>(pfs);
}
#line 3 "/home/maspy/compro/library/nt/three_square.hpp"
// https://math.stackexchange.com/questions/483101/rabin-and-shallit-algorithm
// ERH のもと O(log^2N) ？
tuple<ll, ll, ll> three_square(ll N) {
if (N == 0) return {0, 0, 0};
auto F = [&](ll n) -> tuple<ll, ll, ll> {
if (N == 2) return {1, 1, 0};
if (N == 3) return {1, 1, 1};
if (N == 10) return {3, 1, 0};
if (N == 34) return {5, 3, 0};
if (N == 58) return {7, 3, 0};
if (N == 85) return {9, 2, 0};
if (N == 130) return {11, 3, 0};
if (N == 214) return {14, 3, 3};
if (N == 226) return {15, 1, 0};
if (N == 370) return {19, 3, 0};
if (N == 526) return {21, 9, 2};
if (N == 706) return {25, 9, 0};
if (N == 730) return {27, 1, 0};
if (N == 1414) return {33, 18, 1};
if (N == 1906) return {41, 15, 0};
if (N == 2986) return {45, 31, 0};
if (N == 9634) return {97, 15, 0};
ll x = sqrtl(N);
if (N == x * x) return {x, 0, 0};
if (N % 4 != 1 && x % 2 == 0) --x;
if (N % 4 == 1 && x % 2 == 1) --x;
x += 2;
while (1) {
x -= 2;
ll k = N - x * x;
if (k < 0) break;
if (k % 2 == 1 && primetest(k)) {
auto [a, b] = solve_norm_equation_prime(k);
a = abs(a), b = abs(b);
return {a, b, x};
}
if (k % 2 == 0 && primetest(k / 2)) {
auto [a, b] = solve_norm_equation_prime(k / 2);
tie(a, b) = mp(a + b, a - b);
a = abs(a), b = abs(b);
return {a, b, x};
}
}
return {-1, -1, -1};
assert(0);
};
ll e = 0;
while (N % 4 == 0) N /= 4, ++e;
if (N % 8 == 7) return {-1, -1, -1};
auto [a, b, c] = F(N);
return {a << e, b << e, c << e};
}
#line 2 "/home/maspy/compro/library/nt/four_square.hpp"
tuple<ll, ll, ll, ll> four_square(ll N) {
if (N == 0) return {0, 0, 0, 0};
ll e = 0;
while (N % 4 == 0) N /= 4, ++e;
auto [a, b, c] = three_square(N);
if (a != -1) return {a << e, b << e, c << e, 0};
tie(a, b, c) = three_square(N - 1);
return {a << e, b << e, c << e, 1LL << e};
}
#line 5 "main.cpp"
void solve() {
LL(N);
auto [a, b, c, d] = four_square(N);
vi ANS;
FOR(4) {
tie(a, b, c, d) = mt(b, c, d, a);
if (a > 0) ANS.eb(a * a);
}
print(len(ANS));
print(ANS);
}
signed main() {
int T = 1;
// INT(T);
FOR(T) solve();
return 0;
}