結果
問題 | No.2120 場合の数の下8桁 |
ユーザー | siganai |
提出日時 | 2022-11-04 22:34:42 |
言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
結果 |
AC
|
実行時間 | 10 ms / 2,000 ms |
コード長 | 8,637 bytes |
コンパイル時間 | 2,735 ms |
コンパイル使用メモリ | 219,952 KB |
実行使用メモリ | 7,936 KB |
最終ジャッジ日時 | 2024-07-18 20:30:01 |
合計ジャッジ時間 | 3,542 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge2 |
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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 | 10 ms
7,808 KB |
testcase_01 | AC | 9 ms
7,808 KB |
testcase_02 | AC | 10 ms
7,808 KB |
testcase_03 | AC | 10 ms
7,808 KB |
testcase_04 | AC | 10 ms
7,808 KB |
testcase_05 | AC | 10 ms
7,808 KB |
testcase_06 | AC | 10 ms
7,936 KB |
testcase_07 | AC | 10 ms
7,808 KB |
testcase_08 | AC | 9 ms
7,680 KB |
testcase_09 | AC | 10 ms
7,808 KB |
testcase_10 | AC | 9 ms
7,808 KB |
testcase_11 | AC | 10 ms
7,808 KB |
testcase_12 | AC | 9 ms
7,808 KB |
testcase_13 | AC | 10 ms
7,808 KB |
testcase_14 | AC | 10 ms
7,808 KB |
testcase_15 | AC | 10 ms
7,808 KB |
testcase_16 | AC | 9 ms
7,808 KB |
testcase_17 | AC | 10 ms
7,680 KB |
testcase_18 | AC | 10 ms
7,808 KB |
testcase_19 | AC | 9 ms
7,808 KB |
ソースコード
#line 1 "test.cpp" //#pragma GCC target("avx") //#pragma GCC optimize("O3") //#pragma GCC optimize("unroll-loops") #include <bits/stdc++.h> #ifdef LOCAL #include <debug.hpp> #define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__) #else #define debug(...) (static_cast<void>(0)) #endif using namespace std; using ll = long long; using ld = long double; using pll = pair<ll,ll>; using pii = pair<int,int>; using vi = vector<int>; using vvi = vector<vi>; using vvvi = vector<vvi>; using vl = vector<ll>; using vvl = vector<vl>; using vvvl = vector<vvl>; using vpii = vector<pii>; using vpll = vector<pll>; using vs = vector<string>; template<class T> using pq = priority_queue<T,vector<T>,greater<T>>; #define overload4(_1, _2, _3, _4, name, ...) name #define overload3(a,b,c,name,...) name #define rep1(n) for (ll UNUSED_NUMBER = 0; UNUSED_NUMBER < (n); ++UNUSED_NUMBER) #define rep2(i, n) for (ll i = 0; i < (n); ++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 rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__) #define rrep1(n) for(ll i = (n) - 1;i >= 0;i--) #define rrep2(i,n) for(ll i = (n) - 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 = (a) + ((b)-(a)-1) / (c) * (c);i >= (a);i -= c) #define rrep(...) overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__) #define all1(i) begin(i),end(i) #define all2(i,a) begin(i),begin(i)+a #define all3(i,a,b) begin(i)+a,begin(i)+b #define all(...) overload3(__VA_ARGS__, all3, all2, all1)(__VA_ARGS__) #define sum(...) accumulate(all(__VA_ARGS__),0LL) template<class T> bool chmin(T &a, const T &b){ if(a > b){ a = b; return 1; } else return 0; } template<class T> bool chmax(T &a, const T &b){ if(a < b){ a = b; return 1; } else return 0; } template<class T> auto min(const T& a){ return *min_element(all(a)); } template<class T> auto max(const T& a){ return *max_element(all(a)); } template<class... Ts> void in(Ts&... t); #define INT(...) int __VA_ARGS__; in(__VA_ARGS__) #define LL(...) ll __VA_ARGS__; in(__VA_ARGS__) #define STR(...) string __VA_ARGS__; in(__VA_ARGS__) #define CHR(...) char __VA_ARGS__; in(__VA_ARGS__) #define DBL(...) double __VA_ARGS__; in(__VA_ARGS__) #define LD(...) ld __VA_ARGS__; in(__VA_ARGS__) #define VEC(type, name, size) vector<type> name(size); in(name) #define VV(type, name, h, w) vector<vector<type>> name(h, vector<type>(w)); in(name) ll intpow(ll a, ll b){ ll ans = 1; while(b){if(b & 1) ans *= a; a *= a; b /= 2;} return ans;} ll modpow(ll a, ll b, ll p){ ll ans = 1; a %= p;while(b){ if(b & 1) (ans *= a) %= p; (a *= a) %= p; b /= 2; } return ans; } ll GCD(ll a,ll b) { if(a == 0 || b == 0) return a + b; if(a % b == 0) return b; else return GCD(b,a%b);} ll LCM(ll a,ll b) { if(a == 0) return b; if(b == 0) return a;return a / GCD(a,b) * b;} namespace IO{ #define VOID(a) decltype(void(a)) struct setting{ setting(){cin.tie(nullptr); ios::sync_with_stdio(false);fixed(cout); cout.precision(12);}} setting; template<int I> struct P : P<I-1>{}; template<> struct P<0>{}; template<class T> void i(T& t){ i(t, P<3>{}); } void i(vector<bool>::reference t, P<3>){ int a; i(a); t = a; } template<class T> auto i(T& t, P<2>) -> VOID(cin >> t){ cin >> t; } template<class T> auto i(T& t, P<1>) -> VOID(begin(t)){ for(auto&& x : t) i(x); } template<class T, size_t... idx> void ituple(T& t, index_sequence<idx...>){ in(get<idx>(t)...);} template<class T> auto i(T& t, P<0>) -> VOID(tuple_size<T>{}){ ituple(t, make_index_sequence<tuple_size<T>::value>{});} #undef VOID } #define unpack(a) (void)initializer_list<int>{(a, 0)...} template<class... Ts> void in(Ts&... t){ unpack(IO :: i(t)); } #undef unpack constexpr int mod = 1000000007; //constexpr int mod = 998244353; static const double PI = 3.1415926535897932; template <class F> struct REC { F f; REC(F &&f_) : f(forward<F>(f_)) {} template <class... Args> auto operator()(Args &&...args) const { return f(*this, forward<Args>(args)...); }}; #include <atcoder/math.hpp> #line 3 "library/modint/barrett-reduction.hpp" using namespace std; struct Barrett { using u32 = unsigned int; using i64 = long long; using u64 = unsigned long long; u32 m; u64 im; Barrett() : m(), im() {} Barrett(int n) : m(n), im(u64(-1) / m + 1) {} constexpr inline i64 quo(u64 n) { u64 x = u64((__uint128_t(n) * im) >> 64); u32 r = n - x * m; return m <= r ? x - 1 : x; } constexpr inline i64 rem(u64 n) { u64 x = u64((__uint128_t(n) * im) >> 64); u32 r = n - x * m; return m <= r ? r + m : r; } constexpr inline pair<i64, int> quorem(u64 n) { u64 x = u64((__uint128_t(n) * im) >> 64); u32 r = n - x * m; if (m <= r) return {x - 1, r + m}; return {x, r}; } constexpr inline i64 pow(u64 n, i64 p) { u32 a = rem(n), r = m == 1 ? 0 : 1; while (p) { if (p & 1) r = rem(u64(r) * a); a = rem(u64(a) * a); p >>= 1; } return r; } }; #line 88 "test.cpp" #define PRIME_POWER_BINOMIAL_M_MAX ((1LL << 30) - 1) #define PRIME_POWER_BINOMIAL_N_MAX 20000000 struct prime_power_binomial { int p, q, M; vector<int> fac, ifac, inv; int delta; Barrett bm, bp; prime_power_binomial(int _p, int _q) : p(_p), q(_q) { assert(1 < p && p <= PRIME_POWER_BINOMIAL_M_MAX); assert(_q > 0); long long m = 1; while (_q--) { m *= p; assert(m <= PRIME_POWER_BINOMIAL_M_MAX); } M = m; bm = Barrett(M), bp = Barrett(p); enumerate(); delta = (p == 2 && q >= 3) ? 1 : M - 1; } void enumerate() { int MX = min<int>(M, PRIME_POWER_BINOMIAL_N_MAX + 10); fac.resize(MX); ifac.resize(MX); inv.resize(MX); fac[0] = ifac[0] = inv[0] = 1; fac[1] = ifac[1] = inv[1] = 1; for (int i = 2; i < MX; i++) { if (i % p == 0) { fac[i] = fac[i - 1]; fac[i + 1] = bm.rem(1LL * fac[i - 1] * (i + 1)); i++; } else { fac[i] = bm.rem(1LL * fac[i - 1] * i); } } ifac[MX - 1] = bm.pow(fac[MX - 1], M / p * (p - 1) - 1); for (int i = MX - 2; i > 1; --i) { if (i % p == 0) { ifac[i] = bm.rem(1LL * ifac[i + 1] * (i + 1)); ifac[i - 1] = ifac[i]; i--; } else { ifac[i] = bm.rem(1LL * ifac[i + 1] * (i + 1)); } } } long long Lucas(long long n, long long m) { int res = 1; while (n) { int n0, m0; tie(n, n0) = bp.quorem(n); tie(m, m0) = bp.quorem(m); if (n0 < m0) return 0; res = bm.rem(1LL * res * fac[n0]); int buf = bm.rem(1LL * ifac[n0 - m0] * ifac[m0]); res = bm.rem(1LL * res * buf); } return res; } long long C(long long n, long long m) { if (n < m || n < 0 || m < 0) return 0; if (q == 1) return Lucas(n, m); long long r = n - m; int e0 = 0, eq = 0, i = 0; int res = 1; while (n) { res = bm.rem(1LL * res * fac[bm.rem(n)]); res = bm.rem(1LL * res * ifac[bm.rem(m)]); res = bm.rem(1LL * res * ifac[bm.rem(r)]); n = bp.quo(n); m = bp.quo(m); r = bp.quo(r); int eps = n - m - r; e0 += eps; if (e0 >= q) return 0; if (++i >= q) eq += eps; } if (eq & 1) res = bm.rem(1LL * res * delta); res = bm.rem(1LL * res * bm.pow(p, e0)); return res; } }; // constraints: // (M <= 1e7 and max(N) <= 1e18) or (M < 2^30 and max(N) <= 2e7) struct arbitrary_mod_binomial { int mod; vector<int> M; vector<prime_power_binomial> cs; arbitrary_mod_binomial(long long md) : mod(md) { assert(1 <= md); assert(md <= PRIME_POWER_BINOMIAL_M_MAX); for (int i = 2; i * i <= md; i++) { if (md % i == 0) { int j = 0, k = 1; while (md % i == 0) md /= i, j++, k *= i; M.push_back(k); cs.emplace_back(i, j); assert(M.back() == cs.back().M); } } if (md != 1) { M.push_back(md); cs.emplace_back(md, 1); } assert(M.size() == cs.size()); } long long C(long long n, long long m) { if (mod == 1) return 0; vector<long long> rem, d; for (int i = 0; i < (int)cs.size(); i++) { rem.push_back(cs[i].C(n, m)); d.push_back(M[i]); } return atcoder::crt(rem, d).first; } }; #undef PRIME_POWER_BINOMIAL_M_MAX #undef PRIME_POWER_BINOMIAL_N_MAX int main() { INT(m,n); arbitrary_mod_binomial C(100000000); string ans = to_string(C.C(m,n)); rep(i,8-(int)ans.size()) cout << 0; cout << ans << '\n'; }