結果
| 問題 | No.3333 Consecutive Power Sum (Large) |
| コンテスト | |
| ユーザー |
 apricity
|
| 提出日時 | 2026-01-26 22:22:24 |
| 言語 | C++23 (gcc 15.2.0 + boost 1.89.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 16,712 bytes |
| 記録 | |
| コンパイル時間 | 4,788 ms |
| コンパイル使用メモリ | 327,008 KB |
| 実行使用メモリ | 18,580 KB |
| 最終ジャッジ日時 | 2026-01-26 22:22:49 |
| 合計ジャッジ時間 | 24,068 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge4 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 4 TLE * 1 -- * 58 |
ソースコード
#include<iostream>
#include<string>
#include<vector>
#include<algorithm>
#include<numeric>
#include<cmath>
#include<utility>
#include<tuple>
#include<array>
#include<cstdint>
#include<cstdio>
#include<iomanip>
#include<map>
#include<set>
#include<unordered_map>
#include<unordered_set>
#include<queue>
#include<stack>
#include<deque>
#include<bitset>
#include<cctype>
#include<chrono>
#include<random>
#include<cassert>
#include<cstddef>
#include<iterator>
#include<string_view>
#include<type_traits>
#include<functional>
using namespace std;
#include <cstring>
#include <unistd.h>
#include <sys/mman.h>
#include <sys/stat.h>
namespace fastio {
#ifndef FAST_IO
#define FAST_IO
#endif
struct Pre {
char num[10000][4];
constexpr Pre() : num() {
for (int i = 0; i < 10000; i++) {
int n = i;
for (int j = 3; j >= 0; j--) {
num[i][j] = n % 10 | '0';
n /= 10;
}
}
}
} constexpr pre;
static constexpr int BUF_SZ = 1 << 18;
char *ibuf, obuf[BUF_SZ], outs[100];
int outi, obufi;
void __attribute__((constructor)) _c() {
struct stat sb;
fstat(0, &sb);
ibuf = (char *)mmap(0, sb.st_size, PROT_READ, MAP_SHARED /*| MAP_POPULATE*/, 0, 0);
}
void flush() { write(1, obuf, obufi), obufi = 0; }
void input(char &c) { c = *ibuf++; }
void input(string &x) {
x.clear();
char c;
do { input(c); } while (isspace(c));
do { x += c, input(c); } while (!isspace(c));
}
template <typename T>
void input_integer(T &x) {
char c;
do { input(c); } while (c < '-');
bool minus = 0;
if constexpr (is_signed<T>::value || is_same_v<T, __int128>) {
if (c == '-') { minus = 1, input(c); }
}
x = 0;
while (c >= '0') { x = x * 10 + (c & 15), input(c); }
if constexpr (is_signed<T>::value || is_same_v<T, __int128>) {
if (minus) { x = -x; }
}
}
template <typename T>
void input_real(T &x) { string s; input(s); x = stod(s); }
void input(int &x) { input_integer(x); }
void input(long long &x) { input_integer(x); }
void input(__int128 &x) { input_integer(x); }
void input(uint32_t &x) { input_integer(x); }
void input(uint64_t &x) { input_integer(x); }
void input(unsigned __int128 &x) { input_integer(x); }
void input(double &x) { input_real(x); }
template <class T>
void input(vector<T> &x) { for (auto &d : x) input(d); }
template <typename T, size_t N = 0>
void input(array<T, N> &x) { for (auto &d : x) input(d); }
template <class T, class U>
void input(pair<T, U> &p) { input(p.first), input(p.second); }
template <size_t N = 0, typename T>
void input_tuple(T &t) {
if constexpr (N < std::tuple_size<T>::value) {
auto &x = std::get<N>(t);
input(x);
input_tuple<N + 1>(t);
}
}
template <class... T>
void input(tuple<T...> &tpl) { input_tuple(tpl); }
void in() {}
template <class H, class... T>
void in(H &h, T &... t) { input(h), in(t...); }
void output(const char c) {
if (obufi == BUF_SZ) flush();
obuf[obufi++] = c;
}
void output(const string &s) { for (char c : s) output(c); }
template <typename T>
void output_integer(T x) {
if (obufi > BUF_SZ - 100) flush();
if (x < 0) { obuf[obufi++] = '-', x = -x; }
for (outi = 96; x >= 10000; outi -= 4) {
memcpy(outs + outi, pre.num[x % 10000], 4);
x /= 10000;
}
if (x >= 1000) {
memcpy(obuf + obufi, pre.num[x], 4);
obufi += 4;
}
else if (x >= 100) {
memcpy(obuf + obufi, pre.num[x] + 1, 3);
obufi += 3;
}
else if(x >= 10) {
int q = (x * 103) >> 10;
obuf[obufi] = q | '0';
obuf[obufi + 1] = (x - q * 10) | '0';
obufi += 2;
}
else {
obuf[obufi++] = x | '0';
}
memcpy(obuf + obufi, outs + outi + 4, 96 - outi);
obufi += 96 - outi;
}
template <typename T>
void output_real(T x) {
ostringstream oss;
oss << fixed << setprecision(15) << double(x);
string s = oss.str();
output(s);
}
void output(int x) { output_integer(x); }
void output(long long x) { output_integer(x); }
void output(size_t x) { output_integer(x); }
void output(__int128 x) { output_integer(x); }
void output(uint32_t x) { output_integer(x); }
// void output(uint64_t x) { output_integer(x); }
void output(unsigned __int128 x) { output_integer(x); }
void output(double x) { output_real(x); }
void output(long double x) { output_real(x); }
template <class T>
void output(const vector<T> &val) {
size_t n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) output(' ');
output(val[i]);
}
}
template <class T, class U>
void output(const pair<T, U> &val) {
output(val.first); output(' '); output(val.second);
}
template <size_t N = 0, typename T>
void output_tuple(const T &t) {
if constexpr (N < std::tuple_size<T>::value) {
if constexpr (N > 0) { output(' '); }
const auto x = std::get<N>(t);
output(x);
output_tuple<N+1>(t);
}
}
template <class... T>
void output(tuple<T...> &tpl) { output_tuple(tpl); }
template <class T, size_t N>
void output(const array<T, N> &val) {
size_t n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) output(' ');
output(val[i]);
}
}
void out() { output('\n'); }
template <class H, class... T, char sep = ' '>
void out(H &&h, T &&... t) {
output(h);
if (sizeof...(T)) output(sep);
out(t...);
}
void outr() {}
template <class H, class... T>
void outr(H &&h, T &&... t) {
output(h);
outr(t...);
}
void __attribute__((destructor)) _d() { flush(); }
} // namespace fastio
using fastio::in;
using fastio::out;
#define SHOW(x) static_cast<void>(0)
using ll = long long;
using D = double;
using LD = long double;
using P = pair<ll, ll>;
using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using i128 = __int128;
using u128 = unsigned __int128;
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>>;
#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__))))
template<typename T> using PQ = priority_queue<T,vector<T>>;
template<typename T> using minPQ = priority_queue<T, vector<T>, greater<T>>;
#define rep1(a) for(ll i = 0; i < a; i++)
#define rep2(i, a) for(ll i = 0; i < a; i++)
#define rep3(i, a, b) for(ll i = a; i < b; i++)
#define rep4(i, a, b, c) for(ll i = a; i < b; i += c)
#define overload4(a, b, c, d, e, ...) e
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define rrep1(a) for(ll i = (a)-1; i >= 0; i--)
#define rrep2(i, a) for(ll i = (a)-1; i >= 0; i--)
#define rrep3(i, a, b) for(ll i = (b)-1; i >= a; i--)
#define rrep4(i, a, b, c) for(ll i = (b)-1; i >= a; i -= c)
#define rrep(...) overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__)
#define for_subset(t, s) for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define ALL(v) v.begin(), v.end()
#define RALL(v) v.rbegin(), v.rend()
#define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() )
#define SZ(v) ll(v.size())
#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)))
template <typename T, typename U>
T SUM(const vector<U> &v) {
T res = 0;
for(auto &&a : v) res += a;
return res;
}
template <typename T>
vector<pair<T,int>> RLE(const vector<T> &v) {
if (v.empty()) return {};
T cur = v.front();
int cnt = 1;
vector<pair<T,int>> res;
for (int i = 1; i < (int)v.size(); i++) {
if (cur == v[i]) cnt++;
else {
res.emplace_back(cur, cnt);
cnt = 1; cur = v[i];
}
}
res.emplace_back(cur, cnt);
return res;
}
template<class T, class S>
inline bool chmax(T &a, const S &b) { return (a < b ? a = b, true : false); }
template<class T, class S>
inline bool chmin(T &a, const S &b) { return (a > b ? a = b, true : false); }
void YESNO(bool flag) { out(flag ? "YES" : "NO"); }
void yesno(bool flag) { out(flag ? "Yes" : "No"); }
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_sgn(int x) { return (__builtin_parity(x) & 1 ? -1 : 1); }
int popcnt_sgn(u32 x) { return (__builtin_parity(x) & 1 ? -1 : 1); }
int popcnt_sgn(ll x) { return (__builtin_parityl(x) & 1 ? -1 : 1); }
int popcnt_sgn(u64 x) { return (__builtin_parityl(x) & 1 ? -1 : 1); }
int highbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int highbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int highbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int highbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
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>
T get_bit(T x, int k) { return x >> k & 1; }
template <typename T>
T set_bit(T x, int k) { return x | T(1) << k; }
template <typename T>
T reset_bit(T x, int k) { return x & ~(T(1) << k); }
template <typename T>
T flip_bit(T x, int k) { return x ^ T(1) << k; }
template <typename T>
T popf(deque<T> &que) { T a = que.front(); que.pop_front(); return a; }
template <typename T>
T popb(deque<T> &que) { T a = que.back(); que.pop_back(); return a; }
template <typename T>
T pop(queue<T> &que) { T a = que.front(); que.pop(); return a; }
template <typename T>
T pop(stack<T> &que) { T a = que.top(); que.pop(); return a; }
template <typename T>
T pop(PQ<T> &que) { T a = que.top(); que.pop(); return a; }
template <typename T>
T pop(minPQ<T> &que) { T a = que.top(); que.pop(); return a; }
template <typename F>
i128 binary_search(F check, i128 ok, i128 ng, bool check_ok = true) {
if (check_ok) assert(check(ok));
while (ng - ok > 1) {
i128 mid = (ok + ng) / 2;
(check(mid) ? ok : ng) = mid;
}
return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 60) {
for (int _ = 0; _ < iter; _++) {
double mid = (ok + ng) / 2;
(check(mid) ? ok : ng) = mid;
}
return (ok + ng) / 2;
}
// max x s.t. b*x <= a
ll div_floor(ll a, ll b) {
assert(b != 0);
if (b < 0) a = -a, b = -b;
return a / b - (a % b < 0);
}
// max x s.t. b*x < a
ll div_under(ll a, ll b) {
assert(b != 0);
if (b < 0) a = -a, b = -b;
return a / b - (a % b <= 0);
}
// min x s.t. b*x >= a
ll div_ceil(ll a, ll b) {
assert(b != 0);
if (b < 0) a = -a, b = -b;
return a / b + (a % b > 0);
}
// min x s.t. b*x > a
ll div_over(ll a, ll b) {
assert(b != 0);
if (b < 0) a = -a, b = -b;
return a / b + (a % b >= 0);
}
// x = a mod b (b > 0), 0 <= x < b
ll modulo(ll a, ll b) {
assert(b > 0);
ll c = a % b;
return c < 0 ? c + b : c;
}
// (q,r) s.t. a = b*q + r, 0 <= r < b (b > 0)
// div_floor(a,b), modulo(a,b)
pair<ll,ll> divmod(ll a, ll b) {
ll q = div_floor(a,b);
return {q, a - b*q};
}
const vc<int> witness{2,3,5,7,11,13,17,19,23,29,31,37,41};
i128 wp[13][80];
// mod < 2^{80}
i128 mul(i128 a, i128 b, i128 mod) {
array<ll, 3> ar{}, br{};
rep(i,3) ar[i] = (a>>(30*i)) & ((1<<30)-1);
rep(i,3) br[i] = (b>>(30*i)) & ((1<<30)-1);
i128 ans = ar[2]*br[2];
ans = ((ans << 30) + ar[2]*br[1] + ar[1]*br[2]) % mod;
ans = ((ans << 30) + ar[0]*br[2] + ar[1]*br[1] + ar[2]*br[0]) % mod;
ans = ((ans << 30) + ar[0]*br[1] + ar[1]*br[0]) % mod;
return ((ans << 30) + ar[0]*br[0]) % mod;
}
i128 pow_mod(i128 ai, i128 d, i128 mod) {
i128 ret = 1;
int x = 0;
while(d){
if(d&1) ret = mul(ret, wp[ai][x], mod);
d >>= 1;
x++;
}
return ret;
}
int trz(i128 x){
static constexpr u64 msk = (u64)0-1;
u64 h = x>>64, l = (u128)x&(u128)msk;
if(l == 0) return countr_zero(h) + 64;
return countr_zero(l);
}
i128 bgcd(i128 x, i128 y) {
if(x == 0 or y == 0) return x + y;
int n = trz(x), m = trz(y);
x >>= n, y >>= m;
while(x != y){
if(x > y) x = (x-y) >> trz(x-y);
else y = (y-x) >> trz(y-x);
}
return x << min(n,m);
}
bool miller_rabin(i128 n) {
int s = 0, t;
i128 d = n - 1;
while (d % 2 == 0) d >>= 1, s++;
rep(i,13){
i128 a = witness[i];
if (n <= a) return true;
i128 x = pow_mod(i, d, n);
if (x != 1) {
for (t = 0; t < s; t++) {
if (x == n-1) break;
x = mul(x, x, n);
}
if (t == s) return false;
}
}
return true;
}
i128 pollard_rho(i128 n) {
if (n % 2 == 0) return 2;
i128 c = 1;
while(true) {
auto f = [&] (i128 x) { return (mul(x,x,n)+c)%n; };
i128 x = c, y = f(x);
while (true) {
i128 g = bgcd(y-x+n, n);
if(g == 0 or g == n) break;
if(g != 1){
return g;
}
x = f(x);
y = f(f(y));
}
}
}
vector<pair<i128, int>> factorize(i128 n) {
vector<pair<i128, int>> res;
while (n > 1 and !miller_rabin(n)) {
ll p = pollard_rho(n);
int e = 0;
while (n % p == 0) {
n /= p;
e++;
}
res.emplace_back(p, e);
}
if (n > 1) res.emplace_back(n, 1);
return res;
}
vector<i128> divisor(i128 n) {
vector<i128> res{1};
const auto pf = factorize(n);
for (const auto& [p, e] : pf) {
int s = res.size();
for (int i = 0; i < s; i++) {
i128 m = 1;
for (int _ = 0; _ < e; _++) {
m *= p;
res.push_back(res[i]*m);
}
}
}
return res;
}
i128 n;
vc<tuple<int,i128,i128>> ans1, ans2, ans3;
constexpr i128 INF = (i128)1 << 80;
void precalc(){
rep(i,13){
wp[i][0] = witness[i];
rep(j,1,80) wp[i][j] = mul(wp[i][j-1], wp[i][j-1], n);
}
}
i128 sat_pow(i128 a, i128 e){
i128 ret = 1;
rep(_,e){
if(ret >= (INF+a-1)/a) return INF;
ret *= a;
if(ret >= INF) return INF;
}
return ret;
}
void fix_e(int e){
i128 s = 0;
i128 r = 1;
i128 llim = 1;
while(sat_pow(llim, e) <= n) llim++;
vc<i128> pw(llim);
rep(i,1,llim) pw[i] = sat_pow(i,e);
rep(l,1,llim){
while(r < llim and s+pw[r] <= n) s += pw[r++];
if(s == n) ans3.emplace_back(e,l,r-1);
s -= pw[l];
}
}
vc<i128> divs;
void e1(){
vc<i128> div{divs};
for(auto &x : divs) div.emplace_back(x*2);
sort(ALL(div)); UNIQUE(div);
for(auto d : div) {
i128 x = d, y = n*2/d;
if((x&1) != (y&1) and x <= y) ans1.emplace_back(1, (y-x+1)/2, (y+x-1)/2);
}
}
void e2(){
auto check = [&] (i128 len) {
i128 l = binary_search([&](i128 x){
return (x+len-1)*(x+len)*((x+len)*2-1) - (x-1)*x*(2*x-1) <= 6*n;
}, 1, (i128)190000000, false);
if((l+len-1)*(l+len)*((l+len)*2-1) - (l-1)*l*(2*l-1) == 6*n) ans2.emplace_back(2, l, l+len-1);
};
vc<i128> div{divs};
for(auto &x : divs) div.emplace_back(x*2), div.emplace_back(x*3), div.emplace_back(x*6);
sort(ALL(div)); UNIQUE(div);
for(auto d : div) {
check(d);
}
}
void e3(){
i128 s = 0;
i128 r = 1;
for(i128 l = 1; l <= 100000000; l++){
while(s+r*r*r <= n) s += r*r*r, r++;
if(s == n) ans3.emplace_back(3,l,r-1);
s -= l*l*l;
}
}
void solve() {
string ns; in(ns);
for(char c : ns) n = n * 10 + c-'0';
precalc();
divs = divisor(n);
e1();
e2();
e3();
rep(e,4,80) fix_e(e);
out(ans1.size() + ans2.size() + ans3.size());
sort(ALL(ans1));
sort(ALL(ans2));
for (auto x : ans1) out(x);
for (auto x : ans2) out(x);
for (auto x : ans3) out(x);
}
int main() {
int tc = 1;
// in(tc);
while(tc--){
solve();
}
}