結果
問題 | No.1260 たくさんの多項式 |
ユーザー |
![]() |
提出日時 | 2020-10-17 02:26:32 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 115 ms / 2,000 ms |
コード長 | 7,698 bytes |
コンパイル時間 | 1,799 ms |
コンパイル使用メモリ | 198,532 KB |
最終ジャッジ日時 | 2025-01-15 10:28:02 |
ジャッジサーバーID (参考情報) |
judge2 / judge5 |
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ファイルパターン | 結果 |
---|---|
other | AC * 61 |
ソースコード
#include <bits/stdc++.h> using namespace std; using LL = long long int; #define incII(i, l, r) for(LL i = (l) ; i <= (r); i++) #define incIX(i, l, r) for(LL i = (l) ; i < (r); i++) #define incXI(i, l, r) for(LL i = (l) + 1; i <= (r); i++) #define incXX(i, l, r) for(LL i = (l) + 1; i < (r); i++) #define decII(i, l, r) for(LL i = (r) ; i >= (l); i--) #define decIX(i, l, r) for(LL i = (r) - 1; i >= (l); i--) #define decXI(i, l, r) for(LL i = (r) ; i > (l); i--) #define decXX(i, l, r) for(LL i = (r) - 1; i > (l); i--) #define inc(i, n) incIX(i, 0, n) #define dec(i, n) decIX(i, 0, n) #define inc1(i, n) incII(i, 1, n) #define dec1(i, n) decII(i, 1, n) auto inII = [](auto x, auto l, auto r) { return (l <= x && x <= r); }; auto inIX = [](auto x, auto l, auto r) { return (l <= x && x < r); }; auto inXI = [](auto x, auto l, auto r) { return (l < x && x <= r); }; auto inXX = [](auto x, auto l, auto r) { return (l < x && x < r); }; auto setmin = [](auto & a, auto b) { return (b < a ? a = b, true : false); }; auto setmax = [](auto & a, auto b) { return (b > a ? a = b, true : false); }; auto setmineq = [](auto & a, auto b) { return (b <= a ? a = b, true : false); }; auto setmaxeq = [](auto & a, auto b) { return (b >= a ? a = b, true : false); }; #define PB push_back #define EB emplace_back #define MP make_pair #define MT make_tuple #define FI first #define SE second #define FR front() #define BA back() #define ALL(c) c.begin(), c.end() #define RALL(c) c.rbegin(), c.rend() #define RV(c) reverse(ALL(c)) #define SC static_cast #define SI(c) SC<int>(c.size()) #define SL(c) SC<LL >(c.size()) #define RF(e, c) for(auto & e: c) #define SF(c, ...) for(auto & [__VA_ARGS__]: c) #define until(e) while(! (e)) #define if_not(e) if(! (e)) #define ef else if #define UR assert(false) auto * IS = & cin; auto * OS = & cout; array<string, 3> SEQ = { "", " ", "" }; // input template<typename T> T in() { T a; (* IS) >> a; return a; } // input: tuple template<int I, typename U> void tin_(istream & is, U & t) { if constexpr(I < tuple_size<U>::value) { is >> get<I>(t); tin_<I + 1>(is, t); } } template<typename ... T> istream & operator>>(istream & is, tuple<T ...> & t) { tin_<0>(is, t); return is; } template<typename ... T> auto tin() { return in<tuple<T ...>>(); } // input: array template<typename T, size_t N> istream & operator>>(istream & is, array<T, N> & a) { RF(e, a) { is >> e; } return is; } template<typename T, size_t N> auto ain() { return in<array<T, N>>(); } // input: multi-dimensional vector template<typename T> T vin() { T v; (* IS) >> v; return v; } template<typename T, typename N, typename ... M> auto vin(N n, M ... m) { vector<decltype(vin<T, M ...>(m ...))> v(n); inc(i, n) { v[i] = vin<T, M ...>(m ...); } return v; } // input: multi-column (tuple<vector>) template<typename U, int I> void colin_([[maybe_unused]] U & t) { } template<typename U, int I, typename A, typename ... B> void colin_(U & t) { get<I>(t).PB(in<A>()); colin_<U, I + 1, B ...>(t); } template<typename ... T> auto colin(int n) { tuple<vector<T> ...> t; inc(i, n) { colin_<tuple<vector<T> ...>, 0, T ...>(t); } return t; } // output void out_([[maybe_unused]] string s) { } template<typename A> void out_([[maybe_unused]] string s, A && a) { (* OS) << a; } template<typename A, typename ... B> void out_(string s, A && a, B && ... b) { (* OS) << a << s; out_(s, b ...); } auto outF = [](auto x, auto y, auto z, auto ... a) { (* OS) << x; out_(y, a ...); (* OS) << z << flush; }; auto out = [](auto ... a) { outF("", " " , "\n", a ...); }; auto outS = [](auto ... a) { outF("", " " , " " , a ...); }; auto outL = [](auto ... a) { outF("", "\n", "\n", a ...); }; auto outN = [](auto ... a) { outF("", "" , "" , a ...); }; // output: multi-dimensional vector template<typename T> ostream & operator<<(ostream & os, vector<T> const & v) { os << SEQ[0]; inc(i, SI(v)) { os << (i == 0 ? "" : SEQ[1]) << v[i]; } return (os << SEQ[2]); } template<typename T> void vout_(T && v) { (* OS) << v; } template<typename T, typename A, typename ... B> void vout_(T && v, A a, B ... b) { inc(i, SI(v)) { (* OS) << (i == 0 ? "" : a); vout_(v[i], b ...); } } template<typename T, typename A, typename ... B> void vout (T && v, A a, B ... b) { vout_(v, a, b ...); (* OS) << a << flush; } template<typename T, typename A, typename ... B> void voutN(T && v, A a, B ... b) { vout_(v, a, b ...); (* OS) << flush; } // ---- ---- template<LL M> class ModInt { private: LL v; pair<LL, LL> ext_gcd(LL a, LL b) { if(b == 0) { assert(a == 1); return { 1, 0 }; } auto p = ext_gcd(b, a % b); return { p.SE, p.FI - (a / b) * p.SE }; } public: ModInt(LL vv = 0) { v = vv; if(abs(v) >= M) { v %= M; } if(v < 0) { v += M; } } LL val() { return v; } static LL mod() { return M; } ModInt inv() { return ext_gcd(M, v).SE; } ModInt exp(LL b) { ModInt p = 1, a = v; if(b < 0) { a = a.inv(); b = -b; } while(b) { if(b & 1) { p *= a; } a *= a; b >>= 1; } return p; } friend bool operator< (ModInt a, ModInt b) { return (a.v < b.v); } friend bool operator> (ModInt a, ModInt b) { return (a.v > b.v); } friend bool operator<=(ModInt a, ModInt b) { return (a.v <= b.v); } friend bool operator>=(ModInt a, ModInt b) { return (a.v >= b.v); } friend bool operator==(ModInt a, ModInt b) { return (a.v == b.v); } friend bool operator!=(ModInt a, ModInt b) { return (a.v != b.v); } friend ModInt operator+ (ModInt a ) { return ModInt(+a.v); } friend ModInt operator- (ModInt a ) { return ModInt(-a.v); } friend ModInt operator+ (ModInt a, ModInt b) { return ModInt(a.v + b.v); } friend ModInt operator- (ModInt a, ModInt b) { return ModInt(a.v - b.v); } friend ModInt operator* (ModInt a, ModInt b) { return ModInt(a.v * b.v); } friend ModInt operator/ (ModInt a, ModInt b) { return a * b.inv(); } friend ModInt operator^ (ModInt a, LL b) { return a.exp(b); } friend ModInt & operator+=(ModInt & a, ModInt b) { return (a = a + b); } friend ModInt & operator-=(ModInt & a, ModInt b) { return (a = a - b); } friend ModInt & operator*=(ModInt & a, ModInt b) { return (a = a * b); } friend ModInt & operator/=(ModInt & a, ModInt b) { return (a = a / b); } friend ModInt & operator^=(ModInt & a, LL b) { return (a = a ^ b); } friend istream & operator>>(istream & s, ModInt & b) { s >> b.v; b = ModInt(b.v); return s; } friend ostream & operator<<(ostream & s, ModInt b) { return (s << b.v); } }; // ---- using MI = ModInt<1'000'000'007>; int main() { auto mod_sum = [](LL n, LL x) -> array<MI, 2> { assert(n >= 0 && x >= 0); if(n == 0 || x == 0) { return { 0, 0 }; } MI a = 0, b = 0; LL s = 0; inc1(i, n) { if(i * i < n) { s = i; } else { break; } if(i <= x) { a += n % i; b += n / i % i; } else { return { a, b }; } } dec1(d, s) { LL L = n / (d + 1); LL R = n / (d + 0); setmax(L, s); setmin(R, x); MI c = max(0LL, R - L); a += c * n - c * d * (L + 1 + R) / 2; b += c * d; if(R == x) { break; } } a += max(0LL, x - n) * n; return { a, b }; }; /* auto mod_sum_test = [](LL n, LL x) -> array<MI, 2> { MI a = 0, b = 0; inc1(i, x) { a += n % i; b += n / i % i; } return { a, b }; }; inc(i, 100) { inc(j, 100) { auto [a, b] = mod_sum(i, j); auto [A, B] = mod_sum_test(i, j); outS(a - A, b - B); assert(a == A); assert(b == B); } } */ auto n = in<LL>(); auto [a, b] = mod_sum(n, n); MI ans = a + b; incII(i, 2, n) { LL p = i * i; if_not(p <= n) { break; } while(p <= n) { ans += (n / p) % i; p *= i; } } out(ans); }