結果

問題 No.215 素数サイコロと合成数サイコロ (3-Hard)
ユーザー potetisenseipotetisensei
提出日時 2019-10-01 01:49:01
言語 C++11
(gcc 11.4.0)
結果
AC  
実行時間 2,108 ms / 4,000 ms
コード長 12,241 bytes
コンパイル時間 2,244 ms
コンパイル使用メモリ 214,948 KB
実行使用メモリ 10,748 KB
最終ジャッジ日時 2024-10-03 05:33:40
合計ジャッジ時間 8,950 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge4
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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 2,080 ms
10,748 KB
testcase_01 AC 2,108 ms
10,724 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#pragma GCC target ("avx")

#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cassert>
#include <algorithm>
#include <numeric>
#include <random>
#include <vector>
#include <array>
#include <bitset>
#include <queue>
#include <set>
#include <unordered_set>
#include <map>
#include <unordered_map>
#include <complex>
#include <x86intrin.h>

#define ALIGN __attribute__((aligned(32)))

using namespace std;
using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
template<class T> using V = vector<T>;
template<class T> using VV = V<V<T>>;
constexpr ll TEN(int n) { return (n==0) ? 1 : 10*TEN(n-1); }
int bsr(int x) { return 31 - __builtin_clz(x); }
int bsr(ll x) { return 63 - __builtin_clzll(x); }
int bsf(int x) { return __builtin_ctz(x); }
int bsf(ll x) { return __builtin_ctzll(x); }

using C = complex<double>;
namespace std {
  template<>
  C& C::operator*=(const C& y) {
    double a = this->real();
    double b = this->imag();
    double c = y.real();
    double d = y.imag();
    this->real(a*c-b*d);
    this->imag(a*d+b*c);
    return *this;
  }
}

template<class T>
T pow(T x, ll n, T r = 1) {
    while (n) {
        if (n & 1) r *= x;
        x *= x;
        n >>= 1;
    }
    return r;
}

template<uint MD>
struct ModInt {
    uint v;
    ModInt() : v{0} {}
    ModInt(ll v) : v{normS(v%MD+MD)} {}
    explicit operator bool() const {return v != 0;}
    static uint normS(const uint &x) {return (x<MD)?x:x-MD;};
    static ModInt make(const uint &x) {ModInt m; m.v = x; return m;}
    static ModInt inv(const ModInt &x) {return pow(ModInt(x), MD-2);} 
    ModInt operator+(const ModInt &r) const {return make(normS(v+r.v));}
    ModInt operator-(const ModInt &r) const {return make(normS(v+MD-r.v));}
    ModInt operator*(const ModInt &r) const {return make((ull)v*r.v%MD);}
    ModInt operator/(const ModInt &r) const {return *this*inv(r);}
    ModInt& operator+=(const ModInt &r) {return *this=*this+r;}
    ModInt& operator-=(const ModInt &r) {return *this=*this-r;}
    ModInt& operator*=(const ModInt &r) {return *this=*this*r;}
    ModInt& operator/=(const ModInt &r) {return *this=*this/r;}
};
template<uint MD> string to_string(ModInt<MD> m) {return to_string(m.v);}
using Mint = ModInt<TEN(9)+7>;

using R = double;
const R PI = 4*atan(R(1));
using Pc = C;

Pc polar(double r, double t) {
  return Pc(cos(t)*r, sin(t)*r);
}

void fft(bool type, vector<Pc> &c) {
    static vector<Pc> buf[30];
    int N = int(c.size());
    int s = bsr(N);
    assert(1<<s == N);
    if (!buf[s].size()) {
        buf[s] = vector<Pc>(N);
        for (int i = 0; i < N; i++) {
            buf[s][i] = polar(1, i*2*PI/N);
        }
    }
    vector<Pc> a = c, b(N);
    for (int i = 1; i <= s; i++) {
        int W = 1<<(s-i); //変更後の幅W
        for (int y = 0; y < N/2; y += W) {
            Pc now = buf[s][y]; if (type) now.imag(now.imag() * -1);
            for (int x = 0; x < W; x++) {
                auto l =       a[y<<1 | x];
                auto r = now * a[y<<1 | x | W];
                b[y | x]        = l+r;
                b[y | x | N>>1] = l-r;
            }
        }
        swap(a, b);
    }
    c = a;
}

template<class Mint>
vector<Mint> multiply(vector<Mint> x, vector<Mint> y) {
    constexpr int B = 3, SHIFT = 10;
    int S = x.size()+y.size()-1;
    int N = 2<<bsr(S-1);
    vector<Pc> a[B], b[B];
    for (int fe = 0; fe < B; fe++) {
        a[fe] = vector<Pc>(N);
        b[fe] = vector<Pc>(N);
        vector<Pc> c(N);
        for (int i = 0; i < int(x.size()); i++) {
            c[i].real((x[i].v >> (fe*SHIFT)) & ((1<<SHIFT)-1));
        }
        for (int i = 0; i < int(y.size()); i++) {
            c[i].imag((y[i].v >> (fe*SHIFT)) & ((1<<SHIFT)-1));
        }
        fft(false, c);
        for (int i = 0; i < N; i++) {
            c[i] *= 0.5;
        }
        for (int i = 0; i < N; i++) {
            int j = (N-i)%N;
            a[fe][i] = Pc(c[i].real()+c[j].real(), c[i].imag()-c[j].imag());
            b[fe][i] = Pc(c[i].imag()+c[j].imag(), -c[i].real()+c[j].real());
        }
    }
    vector<Mint> z(S);
    vector<Pc> c[B];
    for (int fe = 0; fe < B; fe++) {
        c[fe] = vector<Pc>(N);
    }
    for (int af = 0; af < B; af++) {
        for (int bf = 0; bf < B; bf++) {
            int cf = (af+bf)%B;
            for (int i = 0; i < N; i++) {
                if (af+bf<B) {
                    c[cf][i] += a[af][i]*b[bf][i];
                } else {
                    c[cf][i] += a[af][i]*b[bf][i]*Pc(0, 1);
                }
            }
        }
    }
    for (int fe = 0; fe < B; fe++) {
        fft(true, c[fe]);
    }
    Mint base = 1;
    for (int fe = 0; fe < 2*B-1; fe++) {
        for (int i = 0; i < S; i++) {
            if (fe < B) {
                c[fe][i].real(c[fe][i].real() * 1.0/N);
                z[i] += Mint(ll(round(c[fe][i].real())))*base;
            } else {       
                c[fe-B][i].imag(c[fe-B][i].imag() * 1.0/N);
                z[i] += Mint(ll(round(c[fe-B][i].imag())))*base;
            }
        }
        base *= 1<<SHIFT;
    }
    return z;
}

template<class D>
struct Poly {
    V<D> v;
    int size() const {return int(v.size());}
    Poly(int N = 0) : v(V<D>(N)) {}
    Poly(const V<D> &v) : v(v) {shrink();}
    Poly& shrink() {while (v.size() && !v.back()) v.pop_back(); return *this;}
    D freq(int p) const { return (p < size()) ? v[p] : D(0); }

    Poly operator+(const Poly &r) const {
        int N = size(), M = r.size();
        V<D> res(max(N, M));
        for (int i = 0; i < max(N, M); i++) res[i] = freq(i)+r.freq(i);
        return Poly(res);
    }
    Poly operator-(const Poly &r) const {
        int N = size(), M = r.size();
        V<D> res(max(N, M));
        for (int i = 0; i < max(N, M); i++) res[i] = freq(i)-r.freq(i);
        return Poly(res);
    }
    Poly operator*(const Poly &r) const {
        int N = size(), M = r.size();
        if (min(N, M) == 0) return Poly();
        assert(N+M-1 >= 0);
        V<D> res = multiply(v, r.v);
        return Poly(res);
    }
    Poly operator*(const D &r) const {
        V<D> res(size());
        for (int i = 0; i < size(); i++) res[i] = v[i]*r;
        return Poly(res);
    }
    Poly& operator+=(const Poly &r) {return *this = *this+r;}
    Poly& operator-=(const Poly &r) {return *this = *this-r;}
    Poly& operator*=(const Poly &r) {return *this = *this*r;}
    Poly& operator*=(const D &r) {return *this = *this*r;}

    Poly operator<<(const int n) const {
        assert(n >= 0);
        V<D> res(size()+n);
        for (int i = 0; i < size(); i++) {
            res[i+n] = v[i];
        }
        return Poly(res);
    }
    Poly operator>>(const int n) const {
        assert(n >= 0);
        if (size() <= n) return Poly();
        V<D> res(size()-n);
        for (int i = n; i < size(); i++) {
            res[i-n] = v[i];
        }
        return Poly(res);
    }

    // x % y
    Poly rem(const Poly &y) const {
        return *this - y * div(y);
    }
    Poly rem_inv(const Poly &y, const Poly &ny, int B) const {
        return *this - y * div_inv(ny, B);
    }
    Poly div(const Poly &y) const {
        int B = max(size(), y.size());
        return div_inv(y.inv(B), B);
    }
    Poly div_inv(const Poly &ny, int B) const {
        return (*this*ny)>>(B-1);
    }
    // this * this.inv() = x^n + r(x) (size())
    Poly strip(int n) const {
        V<D> res = v;
        res.resize(min(n, size()));
        return Poly(res);
    }
    Poly rev(int n = -1) const {
        V<D> res = v;
        if (n != -1) res.resize(n);
        reverse(begin(res), end(res));
        return Poly(res);
    }
    // f * f.inv() = x^B + r(x) (B >= n)
    Poly inv(int n) const {
        int N = size();
        assert(N >= 1);
        assert(n >= N-1);
        Poly c = rev();
        Poly d = Poly(V<D>({D(1)/c.freq(0)}));
        int i;
        for (i = 1; i+N-2 < n; i *= 2) {
            auto u = V<D>({2});
            d = (d * (Poly(V<D>{2})-c*d)).strip(2*i);
        }
        return d.rev(n+1-N);
    }
};
template<class D>
string to_string(const Poly<D> &p) {
    if (p.size() == 0) return "0";
    string s = "";
    for (int i = 0; i < p.size(); i++) {
        if (p.v[i]) {
            s += to_string(p.v[i])+"x^"+to_string(i);
            if (i != p.size()-1) s += "+";
        }
    }
    return s;
}
// x^n % mod
template<class D>
Poly<D> nth_mod(ll n, const Poly<D> &mod) {
    int B = mod.size() * 2 - 1;
    Poly<D> mod_inv = mod.inv(B);
    Poly<D> p = V<D>{Mint(1)};
    int m = (!n) ? -1 : bsr(n);
    for (int i = m; i >= 0; i--) {
        if (n & (1LL<<i)) {
            // += 1
            p = (p<<1).rem_inv(mod, mod_inv, B);
        }
        if (i) {
            // *= 2
            p = (p*p).rem_inv(mod, mod_inv, B);
        }
    }
    return p;
}

template<class D>
Poly<D> berlekamp_massey(const V<D> &s) {
    int N = int(s.size());
    V<D> b = {D(1)}, c = {D(1)};
    D y = D(1);
    for (int ed = 1; ed <= N; ed++) {
        int L = int(c.size()), M = int(b.size());
        D x = 0;
        for (int i = 0; i < L; i++) {
            x += c[i]*s[ed-L+i];
        }
        b.push_back(0); M++;
        if (!x) {
            continue;
        }
        D freq = x/y;
        if (L < M) {
            //use b
            auto tmp = c;
            c.insert(begin(c), M-L, D(0));
            for (int i = 0; i < M; i++) {
                c[M-1-i] -= freq*b[M-1-i];
            }
            b = tmp;
            y = x;
        } else {
            //use c
            for (int i = 0; i < M; i++) {
                c[L-1-i] -= freq*b[M-1-i];
            }
        }
    }
    return Poly<D>(c);
}

const int MD = 610 * 13;
const int MC = 310;
const V<int> pd = {2, 3, 5, 7, 11, 13};
const V<int> cd = {4, 6, 8, 9, 10, 12};

struct StopWatch {
    bool f = false;
    clock_t st;
    void start() {
        f = true;
        st = clock();
    }
    int msecs() {
        assert(f);
        return (clock()-st)*1000 / CLOCKS_PER_SEC;
    }
};

int main() {
/*    {
        V<Mint> f = {1, 1, 2, 3};
        cout << to_string(Poly<Mint>(f)) << endl;
        cout << to_string(berlekamp_massey(f)) << endl;
    }*/
    ll n; int x, y;
    cin >> n >> x >> y;
    V<Mint> co(MD+1); co[0] = 1;
    {
        int c = x;
        V<Mint> buf[6];
        for (int i = 0; i < 6; i++) {
            buf[i] = V<Mint>(MD);
            buf[i][0] = 1;
        }
        for (int nc = 0; nc < c; nc++) {
            for (int i = 0; i < 6; i++) {
                for (int nw = MD-1; nw >= 0; nw--) {
                    buf[i][nw] = 0;
                    if (i) buf[i][nw] += buf[i-1][nw];
                    int d = pd[i];
                    if (nw < d) continue;
                    buf[i][nw] += buf[i][nw-d];
                }
            }
        }
        auto co2 = multiply(co, buf[5]);
        co2.resize(co.size());
        co = co2;
    }
    {
        int c = y;
        V<Mint> buf[6];
        for (int i = 0; i < 6; i++) {
            buf[i] = V<Mint>(MD);
            buf[i][0] = 1;
        }
        for (int nc = 0; nc < c; nc++) {
            for (int i = 0; i < 6; i++) {
                for (int nw = MD-1; nw >= 0; nw--) {
                    buf[i][nw] = 0;
                    if (i) buf[i][nw] += buf[i-1][nw];
                    int d = cd[i];
                    if (nw < d) continue;
                    buf[i][nw] += buf[i][nw-d];
                }
            }
        }        
        auto co2 = multiply(co, buf[5]);
        co2.resize(co.size());
        co = co2;
    }
    co[0] = -1;
    auto rco = co;
    reverse(begin(rco), end(rco));
    auto pol = nth_mod(n, Poly<Mint>(rco));
    V<Mint> buf(MD); buf[0] = 1;
    V<Mint> sm(MD);
    for (int i = 0; i < MD; i++) {
        //v[i] * f
        for (int j = 0; j < MD; j++) {
            sm[j] += pol.freq(i)*buf[j];
        }
        for (int j = 1; j < MD; j++) {
            buf[j] += buf[0]*co[j];
        }
        for (int j = 0; j < MD-1; j++) {
            buf[j] = buf[j+1];
        }
        buf[MD-1] = 0;
    }
    Mint ans = 0;
    for (int i = 0; i < MD; i++) {
        ans += sm[i];
    }
    cout << ans.v << endl;
    return 0;
}
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