#423796 (C++14) No.980 Fibonacci Convolution Hard

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問題	No.980 Fibonacci Convolution Hard
ユーザー	ferin
提出日時	2020-01-31 22:02:05
言語	C++14 (gcc 13.3.0 + boost 1.87.0)
結果	MLE
実行時間	-
コード長	12,909 bytes
コンパイル時間	1,862 ms
コンパイル使用メモリ	182,236 KB
実行使用メモリ	855,536 KB
最終ジャッジ日時	2024-09-17 08:12:04
合計ジャッジ時間	8,832 ms
ジャッジサーバーID （参考情報）	judge2 / judge4
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ファイルパターン	結果
other	MLE * 1 -- * 16
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ソースコード

raw source code
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using PII = pair<ll, ll>;
#define FOR(i, a, n) for (ll i = (ll)a; i < (ll)n; ++i)
#define REP(i, n) FOR(i, 0, n)
#define ALL(x) x.begin(), x.end()
template<typename T> void chmin(T &a, const T &b) { a = min(a, b); }
template<typename T> void chmax(T &a, const T &b) { a = max(a, b); }
struct FastIO {FastIO() { cin.tie(0); ios::sync_with_stdio(0); }}fastiofastio;
#ifdef DEBUG_ 
#include "../program_contest_library/memo/dump.hpp"
#else
#define dump(...)
#endif
const ll INF = 1LL<<60;

template<ll MOD>
struct modint {
    ll x;
    modint(): x(0) {}
    modint(ll y) : x(y>=0 ? y%MOD : y%MOD+MOD) {}
    static constexpr ll mod() { return MOD; }
    // e乗
    modint pow(ll e) {
        ll a = 1, p = x;
        while(e > 0) {
            if(e%2 == 0) {p = (p*p) % MOD; e /= 2;}
            else {a = (a*p) % MOD; e--;}
        }
        return modint(a);
    }
    modint inv() const {
        ll a=x, b=MOD, u=1, y=1, v=0, z=0;
        while(a) {
            ll q = b/a;
            swap(z -= q*u, u);
            swap(y -= q*v, v);
            swap(b -= q*a, a);
        }
        return z;
    }
    // Comparators
    bool operator <(modint b) { return x < b.x; }
    bool operator >(modint b) { return x > b.x; }
    bool operator<=(modint b) { return x <= b.x; }
    bool operator>=(modint b) { return x >= b.x; }
    bool operator!=(modint b) { return x != b.x; }
    bool operator==(modint b) { return x == b.x; }
    // Basic Operations
    modint operator+(modint r) const { return modint(*this) += r; }
    modint operator-(modint r) const { return modint(*this) -= r; }
    modint operator*(modint r) const { return modint(*this) *= r; }
    modint operator/(modint r) const { return modint(*this) /= r; }
    modint &operator+=(modint r) {
        if((x += r.x) >= MOD) x -= MOD;
        return *this;
    }
    modint &operator-=(modint r) {
        if((x -= r.x) < 0) x += MOD;
        return *this;
    }
    modint &operator*=(modint r) {
    #if !defined(_WIN32) || defined(_WIN64)
        x = x * r.x % MOD; return *this;
    #endif
        unsigned long long y = x * r.x;
        unsigned xh = (unsigned) (y >> 32), xl = (unsigned) y, d, m;
        asm(
            "divl %4; \n\t"
            : "=a" (d), "=d" (m)
            : "d" (xh), "a" (xl), "r" (MOD)
        );
        x = m;
        return *this;
    }
    modint &operator/=(modint r) { return *this *= r.inv(); }
    // increment, decrement
    modint operator++() { x++; return *this; }
    modint operator++(signed) { modint t = *this; x++; return t; }
    modint operator--() { x--; return *this; }
    modint operator--(signed) { modint t = *this; x--; return t; }
    // 平方剰余のうち一つを返す なければ-1
    friend modint sqrt(modint a) {
        if(a == 0) return 0;
        ll q = MOD-1, s = 0;
        while((q&1)==0) q>>=1, s++;
        modint z=2;
        while(1) {
            if(z.pow((MOD-1)/2) == MOD-1) break;
            z++;
        }
        modint c = z.pow(q), r = a.pow((q+1)/2), t = a.pow(q);
        ll m = s;
        while(t.x>1) {
            modint tp=t;
            ll k=-1;
            FOR(i, 1, m) {
                tp *= tp;
                if(tp == 1) { k=i; break; }
            }
            if(k==-1) return -1;
            modint cp=c;
            REP(i, m-k-1) cp *= cp;
            c = cp*cp, t = c*t, r = cp*r, m = k;
        }
        return r.x;
    }

    template<class T>
    friend modint operator*(T l, modint r) { return modint(l) *= r; }
    template<class T>
    friend modint operator+(T l, modint r) { return modint(l) += r; }
    template<class T>
    friend modint operator-(T l, modint r) { return modint(l) -= r; }
    template<class T>
    friend modint operator/(T l, modint r) { return modint(l) /= r; }
    template<class T>
    friend bool operator==(T l, modint r) { return modint(l) == r; }
    template<class T>
    friend bool operator!=(T l, modint r) { return modint(l) != r; }
    // Input/Output
    friend ostream &operator<<(ostream& os, modint a) { return os << a.x; }
    friend istream &operator>>(istream& is, modint &a) { 
        is >> a.x;
        a.x = ((a.x%MOD)+MOD)%MOD;
        return is;
    }
    friend string to_frac(modint v) {
        static map<ll, PII> mp;
        if(mp.empty()) {
            mp[0] = mp[MOD] = {0, 1};
            FOR(i, 2, 1001) FOR(j, 1, i) if(__gcd(i, j) == 1) {
                mp[(modint(i) / j).x] = {i, j};
            }
        }
        auto itr = mp.lower_bound(v.x);
        if(itr != mp.begin() && v.x - prev(itr)->first < itr->first - v.x) --itr;
        string ret = to_string(itr->second.first + itr->second.second * ((int)v.x - itr->first));
        if(itr->second.second > 1) {
            ret += '/';
            ret += to_string(itr->second.second);
        }
        return ret;
    }
};
using mint = modint<1000000007>;

template<class T, int primitive_root>
struct NTT {
    void ntt(vector<T>& a, int sign) {
        const int n = a.size();
        assert((n^(n&-n)) == 0);
        T g = 3; //g is primitive root of mod
        const ll mod = T::mod();
		T h = g.pow((mod-1)/n); // h^n = 1
		if(sign == -1) h = h.inv(); //h = h^-1 % mod
		//bit reverse
		int i = 0;
		for (int j = 1; j < n - 1; ++j) {
			for (int k = n >> 1; k >(i ^= k); k >>= 1);
			if (j < i) swap(a[i], a[j]);
		}
		for (int m = 1; m < n; m *= 2) {
			const int m2 = 2 * m;
			const T base = h.pow(n/m2);
			T w = 1;
            for(int x=0; x<m; ++x) {
				for (int s = x; s < n; s += m2) {
					T u = a[s];
					T d = a[s + m] * w;
					a[s] = u + d;
					a[s + m] = u - d;
				}
				w *= base;
			}
		}
    }
    void ntt(vector<T>& input) { ntt(input, 1); }
    void inv_ntt(vector<T>& input) {
        ntt(input, -1);
        const T n_inv = T((int)input.size()).inv();
        for(auto &x: input) x *= n_inv;
    }
    vector<T> convolution(const vector<T>& a, const vector<T>& b) {
        int sz = 1;
        while(sz < (int)a.size() + (int)b.size()) sz *= 2;
        vector<T> a2(a), b2(b);
        a2.resize(sz); b2.resize(sz);
        ntt(a2); ntt(b2);
        for(int i=0; i<sz; ++i) a2[i] *= b2[i];
        inv_ntt(a2);
        return a2;
    }
};

template<class T>
vector<T> any_mod_convolution(vector<T> a, vector<T> b) {
    const ll m1 = 167772161, m2 = 469762049, m3 = 1224736769;
    NTT<modint<m1>,3> ntt1;
    NTT<modint<m2>,3> ntt2;
    NTT<modint<m3>,3> ntt3;
    vector<modint<m1>> a1(a.size()), b1(b.size());
    vector<modint<m2>> a2(a.size()), b2(b.size());
    vector<modint<m3>> a3(a.size()), b3(b.size());
    for(int i=0; i<(int)a.size(); ++i) a1[i] = a[i].x, b1[i] = b[i].x;
    for(int i=0; i<(int)a.size(); ++i) a2[i] = a[i].x, b2[i] = b[i].x;
    for(int i=0; i<(int)a.size(); ++i) a3[i] = a[i].x, b3[i] = b[i].x;
    auto x = ntt1.convolution(a1, b1);
    auto y = ntt2.convolution(a2, b2);
    auto z = ntt3.convolution(a3, b3);
    const ll m1_inv_m2 = 104391568;
    const ll m12_inv_m3 = 721017874;
    const ll m12_mod = m1 * m2 % T::mod();
    vector<T> ret(x.size());
    for(int i=0; i<(int)x.size(); ++i) {
        ll v1 = (y[i].x-x[i].x) * m1_inv_m2 % m2;
        if(v1<0) v1 += m2;
        ll v2 = (z[i].x-(x[i].x+m1*v1)%m3) * m12_inv_m3 % m3;
        if(v2<0) v2 += m3;
        ret[i] = x[i].x + m1*v1 + m12_mod*v2;
    }
    return ret;
}

namespace fft {
    using dbl = long double;
    struct num {
        dbl x, y;
        num() { x = y = 0; }
        num(dbl x, dbl y) : x(x), y(y) { }
    };
    inline num operator+(num a, num b) { return num(a.x + b.x, a.y + b.y); }
    inline num operator-(num a, num b) { return num(a.x - b.x, a.y - b.y); }
    inline num operator*(num a, num b) { return num(a.x * b.x - a.y * b.y, a.x * b.y + a.y * b.x); }
    inline num conj(num a) { return num(a.x, -a.y); }

    int base = 1;
    vector<num> roots = {{0, 0}, {1, 0}};
    vector<int> rev = {0, 1};

    const dbl PI = acosl(-1.0);

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

    void fft(vector<num> &a, int n = -1) {
        if (n == -1) n = a.size();
        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++) {
                    num z = a[i+j+k] * roots[j+k];
                    a[i+j+k] = a[i+j] - z;
                    a[i+j] = a[i+j] + z;
                }
            }
        }
    }

    vector<num> fa, fb;
    vector<long long> multiply(vector<int> &a, vector<int> &b) {
        int need = a.size() + b.size() - 1;
        int nbase = 0;
        while ((1 << nbase) < need) nbase++;
        ensure_base(nbase);
        int sz = 1 << nbase;
        if (sz > (int) fa.size()) fa.resize(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] = num(x, y);
        }
        fft(fa, sz);
        num r(0, -0.25 / sz);
        for (int i = 0; i <= (sz >> 1); i++) {
            int j = (sz - i) & (sz - 1);
            num z = (fa[j] * fa[j] - conj(fa[i] * fa[i])) * r;
            if (i != j) fa[j] = (fa[i] * fa[i] - conj(fa[j] * fa[j])) * r;
            fa[i] = z;
        }
        fft(fa, sz);
        vector<long long> res(need);
        for (int i = 0; i < need; i++) res[i] = fa[i].x + 0.5;
        return res;
    }
    template<int m>
    vector<int> multiply_mod(vector<int> &a, vector<int> &b) {
        int need = a.size() + b.size() - 1;
        int nbase = 0;
        while ((1 << nbase) < need) nbase++;
        ensure_base(nbase);
        int sz = 1 << nbase;
        if (sz > (int) fa.size()) {
            fa.resize(sz);
        }
        for (int i = 0; i < (int) a.size(); i++) {
            int x = (a[i] % m + m) % m;
            fa[i] = num(x & ((1 << 15) - 1), x >> 15);
        }
        fill(fa.begin() + a.size(), fa.begin() + sz, num {0, 0});
        fft(fa, sz);
        if (sz > (int) fb.size()) {
            fb.resize(sz);
        }
        for (int i = 0; i < (int) b.size(); i++) {
            int x = (b[i] % m + m) % m;
            fb[i] = num(x & ((1 << 15) - 1), x >> 15);
        }
        fill(fb.begin() + b.size(), fb.begin() + sz, num {0, 0});
        fft(fb, sz);
        dbl ratio = 0.25 / sz;
        num r2(0, -1);
        num r3(ratio, 0);
        num r4(0, -ratio);
        num r5(0, 1);
        for (int i = 0; i <= (sz >> 1); i++) {
            int j = (sz - i) & (sz - 1);
            num a1 = (fa[i] + conj(fa[j]));
            num a2 = (fa[i] - conj(fa[j])) * r2;
            num b1 = (fb[i] + conj(fb[j])) * r3;
            num b2 = (fb[i] - conj(fb[j])) * r4;
            if (i != j) {
                num c1 = (fa[j] + conj(fa[i]));
                num c2 = (fa[j] - conj(fa[i])) * r2;
                num d1 = (fb[j] + conj(fb[i])) * r3;
                num d2 = (fb[j] - conj(fb[i])) * 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<int> res(need);
        for (int i = 0; i < need; i++) {
            long long aa = fa[i].x + 0.5;
            long long bb = fb[i].x + 0.5;
            long long cc = fa[i].y + 0.5;
            res[i] = (aa + ((bb % m) << 15) + ((cc % m) << 30)) % m;
        }
        return res;
    }
    // fft::multiply uses dbl, outputs vector<long long> of rounded values
    // fft::multiply_mod might work for res.size() up to 2^21
    // typedef long double dbl; => up to 2^25 (but takes a lot of memory)
};

int main(void) {
    ll p;
    cin >> p;

    const int m = 2000000, MOD = 1000000007;
    vector<int> a(m+1);
    a[1] = 0, a[2] = 1;
    FOR(i, 3, m+1) a[i] = (a[i-1]*p%MOD + a[i-2]) % MOD;

    // auto v = any_mod_convolution(a, a);
    auto v = fft::multiply_mod<MOD>(a, a);

    ll q;
    cin >> q;
    while(q--) {
        ll x;
        cin >> x;
        cout << v[x] << endl;
    }

    return 0;
}
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