#424147 (C++14) No.980 Fibonacci Convolution Hard

• 問題: No.980 Fibonacci Convolution Hard
• ユーザー: やむなく
• 提出日時: 2020-01-31 22:40:19
• 言語: C++14 (gcc 13.3.0 + boost 1.87.0)
• 結果: WA
• 実行時間: -
• コード長: 8,258 bytes
• コンパイル時間: 1,963 ms
• コンパイル使用メモリ: 184,112 KB
• 実行使用メモリ: 239,936 KB
• 最終ジャッジ日時: 2024-09-17 09:31:00
• 合計ジャッジ時間: 29,893 ms
• ジャッジサーバーID （参考情報）: judge5 / judge2

ファイルパターン	結果
other	WA * 17

ソースコード

//
// Created by yamunaku on 2020/01/31.
//

#include <bits/stdc++.h>

using namespace std;

#define rep(i, n) for(int i = 0; i < (n); i++)
#define repl(i, l, r) for(int i = (l); i < (r); i++)
#define per(i, n) for(int i = ((n)-1); i >= 0; i--)
#define perl(i, l, r) for(int i = ((r)-1); i >= (l); i--)
#define all(x) (x).begin(),(x).end()
#define MOD9 998244353
#define MOD 1000000007
#define IINF 1000000000
#define LINF 1000000000000000000
#define SP <<" "<<
#define CYES cout<<"Yes"<<endl
#define CNO cout<<"No"<<endl
#define CFS cin.tie(0);ios::sync_with_stdio(false)
#define CST(x) cout<<fixed<<setprecision(x)

using ll = long long;
using ld = long double;
using vi = vector<int>;
using mti = vector<vector<int>>;
using vl = vector<ll>;
using mtl = vector<vector<ll>>;
using pi = pair<int, int>;
using pl = pair<ll, ll>;
template<typename T>
using heap = priority_queue<T, vector<T>, function<bool(const T, const T)>>;

template<int mod>
struct ModInt{
    int x;

    ModInt() : x(0){}

    ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod){}

    ModInt &operator+=(const ModInt &p){
        if((x += p.x) >= mod) x -= mod;
        return *this;
    }

    ModInt &operator-=(const ModInt &p){
        if((x += mod - p.x) >= mod) x -= mod;
        return *this;
    }

    ModInt &operator*=(const ModInt &p){
        x = (int) (1LL * x * p.x % mod);
        return *this;
    }

    ModInt &operator/=(const ModInt &p){
        *this *= p.inverse();
        return *this;
    }

    ModInt operator-() const{ return ModInt(-x); }

    ModInt operator+(const ModInt &p) const{ return ModInt(*this) += p; }

    ModInt operator-(const ModInt &p) const{ return ModInt(*this) -= p; }

    ModInt operator*(const ModInt &p) const{ return ModInt(*this) *= p; }

    ModInt operator/(const ModInt &p) const{ return ModInt(*this) /= p; }

    bool operator==(const ModInt &p) const{ return x == p.x; }

    bool operator!=(const ModInt &p) const{ return x != p.x; }

    ModInt inverse() const{
        int 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);
        }
        return ModInt(u);
    }

    ModInt pow(int64_t n) const{
        ModInt ret(1), mul(x);
        while(n > 0){
            if(n & 1) ret *= mul;
            mul *= mul;
            n >>= 1;
        }
        return ret;
    }

    friend ostream &operator<<(ostream &os, const ModInt &p){
        return os << p.x;
    }

    friend istream &operator>>(istream &is, ModInt &a){
        int64_t t;
        is >> t;
        a = ModInt<mod>(t);
        return (is);
    }

    static int get_mod(){ return mod; }
};


namespace FastFourierTransform{
    using real = double;

    struct C{
        real x, y;

        C() : x(0), y(0){}

        C(real x, real y) : x(x), y(y){}

        inline C operator+(const C &c) const{ return C(x + c.x, y + c.y); }

        inline C operator-(const C &c) const{ return C(x - c.x, y - c.y); }

        inline C operator*(const C &c) const{ return C(x * c.x - y * c.y, x * c.y + y * c.x); }

        inline C conj() const{ return C(x, -y); }
    };

    const real PI = acosl(-1);
    int base = 1;
    vector<C> rts = {{0, 0},
                     {1, 0}};
    vector<int> rev = {0, 1};


    void ensure_base(int nbase){
        if(nbase <= base) return;
        rev.resize(1 << nbase);
        rts.resize(1 << nbase);
        for(int i = 0; i < (1 << nbase); i++){
            rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
        }
        while(base < nbase){
            real angle = PI * 2.0 / (1 << (base + 1));
            for(int i = 1 << (base - 1); i < (1 << base); i++){
                rts[i << 1] = rts[i];
                real angle_i = angle * (2 * i + 1 - (1 << base));
                rts[(i << 1) + 1] = C(cos(angle_i), sin(angle_i));
            }
            ++base;
        }
    }

    void fft(vector<C> &a, int n){
        assert((n & (n - 1)) == 0);
        int zeros = __builtin_ctz(n);
        ensure_base(zeros);
        int shift = base - zeros;
        for(int i = 0; i < n; i++){
            if(i < (rev[i] >> shift)){
                swap(a[i], a[rev[i] >> shift]);
            }
        }
        for(int k = 1; k < n; k <<= 1){
            for(int i = 0; i < n; i += 2 * k){
                for(int j = 0; j < k; j++){
                    C z = a[i + j + k] * rts[j + k];
                    a[i + j + k] = a[i + j] - z;
                    a[i + j] = a[i + j] + z;
                }
            }
        }
    }

    vector<int64_t> multiply(const vector<int> &a, const vector<int> &b){
        int need = (int) a.size() + (int) b.size() - 1;
        int nbase = 1;
        while((1 << nbase) < need) nbase++;
        ensure_base(nbase);
        int sz = 1 << nbase;
        vector<C> fa(sz);
        for(int i = 0; i < sz; i++){
            int x = (i < (int) a.size() ? a[i] : 0);
            int y = (i < (int) b.size() ? b[i] : 0);
            fa[i] = C(x, y);
        }
        fft(fa, sz);
        C r(0, -0.25 / (sz >> 1)), s(0, 1), t(0.5, 0);
        for(int i = 0; i <= (sz >> 1); i++){
            int j = (sz - i) & (sz - 1);
            C z = (fa[j] * fa[j] - (fa[i] * fa[i]).conj()) * r;
            fa[j] = (fa[i] * fa[i] - (fa[j] * fa[j]).conj()) * r;
            fa[i] = z;
        }
        for(int i = 0; i < (sz >> 1); i++){
            C A0 = (fa[i] + fa[i + (sz >> 1)]) * t;
            C A1 = (fa[i] - fa[i + (sz >> 1)]) * t * rts[(sz >> 1) + i];
            fa[i] = A0 + A1 * s;
        }
        fft(fa, sz >> 1);
        vector<int64_t> ret(need);
        for(int i = 0; i < need; i++){
            ret[i] = llround(i & 1 ? fa[i >> 1].y : fa[i >> 1].x);
        }
        return ret;
    }
};

template<typename T>
struct ArbitraryModConvolution{
    using real = FastFourierTransform::real;
    using C = FastFourierTransform::C;

    ArbitraryModConvolution() = default;

    vector<T> multiply(const vector<T> &a, const vector<T> &b, int need = -1){
        if(need == -1) need = a.size() + b.size() - 1;
        int nbase = 0;
        while((1 << nbase) < need) nbase++;
        FastFourierTransform::ensure_base(nbase);
        int sz = 1 << nbase;
        vector<C> fa(sz);
        for(int i = 0; i < a.size(); i++){
            fa[i] = C(a[i].x & ((1 << 15) - 1), a[i].x >> 15);
        }
        fft(fa, sz);
        vector<C> fb(sz);
        if(a == b){
            fb = fa;
        }else{
            for(int i = 0; i < b.size(); i++){
                fb[i] = C(b[i].x & ((1 << 15) - 1), b[i].x >> 15);
            }
            fft(fb, sz);
        }
        real ratio = 0.25 / sz;
        C r2(0, -1), r3(ratio, 0), r4(0, -ratio), r5(0, 1);
        for(int i = 0; i <= (sz >> 1); i++){
            int j = (sz - i) & (sz - 1);
            C a1 = (fa[i] + fa[j].conj());
            C a2 = (fa[i] - fa[j].conj()) * r2;
            C b1 = (fb[i] + fb[j].conj()) * r3;
            C b2 = (fb[i] - fb[j].conj()) * r4;
            if(i != j){
                C c1 = (fa[j] + fa[i].conj());
                C c2 = (fa[j] - fa[i].conj()) * r2;
                C d1 = (fb[j] + fb[i].conj()) * r3;
                C d2 = (fb[j] - fb[i].conj()) * r4;
                fa[i] = c1 * d1 + c2 * d2 * r5;
                fb[i] = c1 * d2 + c2 * d1;
            }
            fa[j] = a1 * b1 + a2 * b2 * r5;
            fb[j] = a1 * b2 + a2 * b1;
        }
        fft(fa, sz);
        fft(fb, sz);
        vector<T> ret(need);
        for(int i = 0; i < need; i++){
            int64_t aa = llround(fa[i].x);
            int64_t bb = llround(fb[i].x);
            int64_t cc = llround(fa[i].y);
            aa = T(aa).x, bb = T(bb).x, cc = T(cc).x;
            ret[i] = aa + (bb << 15) + (cc << 30);
        }
        return ret;
    }
};

int main(){
    // CFS;
    ModInt<MOD> p;
    cin >> p;
    vector<ModInt<MOD>> a(2000010);
    a[0] = 0, a[1] = 1;
    repl(i, 2, 2000010){
        a[i] = p * a[i - 1] + a[i - 2];
    }
    ArbitraryModConvolution<ModInt<MOD>> amc;
    vector<ModInt<MOD>> ans = amc.multiply(a, a);
    int q;
    cin >> q;
    rep(i, q){
        ll x;
        cin >> x;
        x -= 2;
        cout << ans[x] << endl;
    }
    return 0;
}