結果

問題 No.8046 yukicoderの過去問
コンテスト
ユーザー Gosu_Hiroo
提出日時 2020-08-03 21:52:32
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 176 ms / 2,000 ms
コード長 12,369 bytes
コンパイル時間 2,853 ms
コンパイル使用メモリ 215,896 KB
最終ジャッジ日時 2025-01-12 13:59:57
ジャッジサーバーID
（参考情報） 		judge3 / judge2
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ファイルパターン 結果
other AC * 9
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ソースコード

diff # 

/**
 * code generated by JHelper
 * More info: https://github.com/AlexeyDmitriev/JHelper
 * @author
 */

#include <bits/stdc++.h>
using namespace std;
using ll = long long;

#pragma GCC optimize("O3")
#pragma GCC target("avx2")
#pragma GCC optimize("unroll-loops")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
//#pragma GCC optimize("Ofast")

#define VI vector<int>
#define G(size_1) vector<vector<int>>(size_1, vector<int>())
#define SZ(x) ((int)(x).size())
#define READ ({int t;cin >> t;t;})
#define PII pair<int, int>

#define FOR(i, _begin, _end) for (__typeof(_end) end = _end, begin = _begin,  i = (begin) - ((begin) > (end)); i != (end) - ((begin) > (end)); i += 1 - 2 * ((begin) > (end)))
#define REP(i, end) for (__typeof(end) i = 0, _len = (end); i < (_len); i += 1)
#define ALL(x) (x).begin(),(x).end()
#define RALL(x) (x).rbegin(),(x).rend()
#define F first
#define S second
#define y0 y3487465
#define y1 y8687969
#define j0 j1347829
#define j1 j234892
#define BIT(n) (1LL<<(n))
#define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() );
#define EB emplace_back
#define PB push_back
#define fcout cout << fixed << setprecision(12)
#define fcerr cerr << fixed << setprecision(12)
#define print(x) cout << (x) << '\n'
#define printE(x) cout << (x) << endl
#define fprint(x) cout << fixed << setprecision(12) << (x) << endl
# define BYE(a) do { cout << (a) << endl; return ; } while (false)

#ifdef DEBUG
#define DBG(args...) { string _s = #args; replace(_s.begin(), _s.end(), ',', ' '); stringstream _ss(_s); istream_iterator<string> _it(_ss); _err(cerr,_it, args); }
#define ERR(x) std::cerr << #x << " = " << x << endl;
#else
#define DBG(x) {};
#define ERR(args...) {};
#endif
void _err(std::ostream& cerr,istream_iterator<string> it) {cerr << endl;}
template<typename T, typename... Args>
void _err(std::ostream& cerr, istream_iterator<string> it, T a, Args... args) {
    cerr << *it << " = " << a << "  ";
    _err(cerr,++it, args...);
}

const double pi = 2 * acos(.0);
const int inf = 0x3f3f3f3f;
const int MOD = 1e9 + 7;

template<class T>bool Chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T>bool Chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }

template <typename T>
istream& operator >> (istream& is, vector<T>& V) {
    for(auto&& ele : V)is >> ele;
    return is;
}

template <typename T>
ostream& operator << (ostream& os, const vector<T> V) {
    os << "[";
    int cnt = 0;
    T curr;
    if(!V.empty()){
        for (int i = 0; i < V.size() - 1; ++i) {
            if(V[i] == curr)cnt ++;
            else cnt = 0;
            if(cnt == 4)os << "... ";
            if(cnt < 4)
                os << i << ":" << V[i] << " ";
            curr = V[i];
        }
        os << V.size() - 1 << ":" << V.back();
    }
    os << "]\n";
    return os;
}

template <typename T, typename U>
ostream& operator << (ostream& os, const pair<T,U> P) {
    os << "(";
    os << P.first << "," << P.second;
    os << ")";
    return os;
}

template <typename T, typename U>
ostream& operator << (ostream& os, const set<T,U> V) {
    os << "{";
    if(!V.empty()){
        auto it = V.begin();
        for (int i = 0; i < V.size() -1; ++i) {
            os << *it << " ";
            it++;
        }
        os << *it;
    }
    os << "}\n";
    return os;
}

template <typename K, typename H, typename P>
ostream& operator << (ostream& os, const unordered_set<K, H, P> V) {
    os << "{";
    if(!V.empty()){
        auto it = V.begin();
        for (int i = 0; i < V.size() -1; ++i) {
            os << *it << " ";
            it++;
        }
        os << *it;
    }
    os << "}\n";
    return os;
}

template <typename K, typename C>
ostream& operator << (ostream& os, const multiset<K, C> V) {
    os << "{";
    if(!V.empty()){
        auto it = V.begin();
        for (int i = 0; i < V.size() -1; ++i) {
            os << *it << " ";
            it++;
        }
        os << *it;
    }
    os << "}";
    return os;
}

template <typename K, typename T, typename C>
ostream& operator << (ostream& os, const map<K,T,C> V) {
    os << "{";
    if(!V.empty()){
        auto it = V.begin();
        for (int i = 0; i < V.size() -1; ++i) {
            os << "(";
            os << it->first << "," << it->second;
            os << ") ";
            it++;
        }
        os << "(";
        os << it->first << "," << it->second;
        os << ")";
    }
    os << "}\n";
    return os;
}

template <typename K, typename T, typename C>
ostream& operator << (ostream& os, const unordered_map<K,T,C> V) {
    os << "{";
    if(!V.empty()){
        auto it = V.begin();
        for (int i = 0; i < V.size() -1; ++i) {
            os << "(";
            os << it->first << "," << it->second;
            os << ") ";
            it++;
        }
        os << "(";
        os << it->first << "," << it->second;
        os << ")";
    }
    os << "}\n";
    return os;
}

template <typename T>
ostream& operator << (ostream& os, const deque<T> V) {
    os << "[";
    if (!V.empty()) {
        for (int i = 0; i < V.size() - 1; ++i) {
            os << V[i] << "->";
        }
        if (!V.empty())os << V.back();
    }
    os << "]\n";
    return os;
};

template <typename T, typename Cont, typename Comp>
ostream& operator << (ostream& os, const priority_queue<T, Cont, Comp> V) {
    priority_queue<T, Cont, Comp> _V = V;
    os << "[";
    if(!_V.empty()){
        while(_V.size() > 1){
            os << _V.top() << "->";
            _V.pop();
        }
        os << _V.top();
    }
    os << "]\n";
    return os;
};

template <class F>
struct y_combinator {
    F f; // the lambda will be stored here

    // a forwarding operator():
    template <class... Args>
    decltype(auto) operator()(Args&&... args) const {
        // we pass ourselves to f, then the arguments.
        // the lambda should take the first argument as `auto&& recurse` or similar.
        return f(*this, std::forward<Args>(args)...);
    }
};
// helper function that deduces the type of the lambda:
template <class F>
y_combinator<std::decay_t<F>> recursive(F&& f){
return {std::forward<F>(f)};
}

struct hash_pair {
    template <class T1, class T2>
    size_t operator()(const pair<T1, T2>& p) const
    {
        auto hash1 = hash<T1>{}(p.first);
        auto hash2 = hash<T2>{}(p.second);
        return hash1 ^ hash2;
    }

};

template <typename T, typename U>
std::vector<T> multi_vector(int n, U v) {
    return std::vector<T>(n, v);
}

template <typename U, typename... Args>
auto multi_vector(int n, Args... args) {
    auto val = multi_vector<U>(std::forward<Args>(args)...);
    return std::vector<decltype(val)>(n, std::move(val));
}
//template <signed M, unsigned T>
namespace FFT {
    const int max_base = 18, maxN = 1 << max_base; // N <= 2e5
    const double PI = acos(-1);
    struct num {
        double x{}, y{};
        num() = default;
        num(double x, double y): x(x), y(y) {}
        explicit num(double r): x(cos(r)), y(sin(r)) {}
    };
    num operator+(num a, num b) { return {a.x + b.x, a.y + b.y}; }
    num operator-(num a, num b) { return {a.x - b.x, a.y - b.y}; }
    num operator*(num a, num b) { return {a.x * b.x - a.y * b.y, a.x * b.y + a.y * b.x}; }
    num conj(num a) {return {a.x, -a.y}; }
    num root[maxN];
    int rev[maxN];
    bool is_root_prepared = false;

    void prepare_root(){
        if(is_root_prepared) return;
        is_root_prepared = true;
        root[1] = num(1, 0);
        for (int i = 1; i < max_base; ++i) {
            num x(2*PI / (1LL << (i+1)));
            for (ll j = (1LL << (i-1)); j < (1LL << (i)); ++j) {
                root[2*j] = root[j];
                root[2*j+1] = root[j]*x;
            }
        }
    }

    int base, N;
    int lastN = -1;

    void prepare_rev(){
        if(lastN == N) return;
        lastN = N;
        for (int i = 0; i < N; ++i) rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (base - 1));
    }

    void fft(num *a, num *f){
        for (int i = 0; i < N; ++i) f[i] = a[rev[i]];
        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 = f[i+j+k]* root[j+k];
                    f[i+j+k] = f[i+j] - z;
                    f[i+j] = f[i+j] + z;
                }
            }
        }
    }
    num a[maxN], b[maxN], f[maxN], g[maxN];
    ll A[maxN], B[maxN], C[maxN];

    void multi_mod(int m){
        for (int i = 0; i < N; ++i) {
            ll x = A[i] % m;
            a[i] = num(x & ((1LL << 15)-1), x >> 15);
        }
        for (int i = 0; i < N; ++i) {
            ll x = B[i] % m;
            b[i] = num(x & ((1LL << 15)-1), x >> 15);
        }
        fft(a, f);
        fft(b, g);
        for (int i = 0; i < N; ++i) {
            int j = (N-i) &(N-1);
            num a1 = (f[i] + conj(f[j])) * num(0.5, 0);
            num a2 = (f[i] - conj(f[j])) * num(0, -0.5);
            num b1 = (g[i] + conj(g[j])) * num(0.5/N, 0);
            num b2 = (g[i] - conj(g[j])) * num(0, -0.5/N);
            a[j] = a1*b1 + a2*b2 * num(0, 1);
            b[j] = a1*b2 + a2*b1;
        }
        fft(a, f);
        fft(b, g);
        for (int i = 0; i < N; ++i) {
            ll aa = f[i].x + 0.5;
            ll bb = g[i].x + 0.5;
            ll cc = f[i].y + 0.5;
            C[i] = (aa + bb % m * (1LL << 15) + cc% m *(1LL << 30)) % m;
        }
    }

    void prepare_AB(int n1, int n2){
        base = 1;
        N = 2;
        while(N < n1+n2) base++, N <<= 1;
        for (int i = n1; i < N; ++i) A[i] = 0;
        for (int i = n2; i < N; ++i) B[i] = 0;
        prepare_root();
        prepare_rev();
    }

    void multi_mod(int n1, int n2, int m){
        prepare_AB(n1, n2);
        multi_mod(m);
    }
}

struct poly {
    vector<int> v;
    poly() = default;
    explicit poly(vector<int> vv) : v(std::move(vv)) {};
    int size() {return (int)v.size(); }
    poly cut(int len){
        if(len < v.size()) v.resize(static_cast<unsigned long>(len));
        return *this;
    }
    inline int& operator[] (int i) {return v[i]; }
};

poly operator+(poly &A, poly &B){
    poly C;
    C.v = vector<int>(max(A.size(), B.size()));
    for (int i = 0; i < A.size(); ++i) C[i] = A[i];
    for (int i = 0; i < B.size(); ++i) (C[i] += B[i]) %= MOD;
    return C;
}

poly operator-(poly &A, poly &B){
    poly C;
    C.v = vector<int>(max(A.size(), B.size()));
    for (int i = 0; i < A.size(); ++i) C[i] = A[i];
    for (int i = 0; i < B.size(); ++i) (C[i] += MOD-B[i]) %= MOD;
    return C;
}

poly operator* (poly &A, poly &B){
    poly C;
    C.v = vector<int>(A.size() + B.size()-1);
    for (int i = 0; i < A.size(); ++i) FFT::A[i] = A[i];
    for (int i = 0; i < B.size(); ++i) FFT::B[i] = B[i];
    FFT::multi_mod(A.size(), B.size(), MOD);
    for (int i = 0; i < C.size(); ++i) C[i] = FFT::C[i];
    return C;
}

template<typename T>
T extgcd(T a, T b, T &x ,T &y){
    for (T u = y = 1, v = x = 0; a; ) {
        ll q = b/a;
        swap(x -= q*u, u);
        swap(y -= q*v, v);
        swap(b -= q*a, a);
    }
    return b;
}

template<typename T>
T mod_inv(T x, T m){
    T s, t;
    extgcd(x, m, s, t);
    return (m+s)% m;
}

poly inv (poly f){
    int n = f.size();
    vector<int> rr(1, mod_inv(f[0], MOD));
    poly r(rr);
    for (int k = 2; k <= n; k <<= 1) {
        vector<int> v(k);
        for (int i = 0; i < k; ++i) {
            v[i] = f[i];
        }
        poly ff(v);
        poly nr = (r*r);
        nr = nr*ff;
        nr.cut(k);
        for (int i = 0; i < k/2; ++i) {
            nr[i] = (2*r[i]-nr[i]+MOD)%MOD;
            nr[i+k/2] = (MOD-nr[i+k/2])%MOD;
        }
        r = nr;
    }
    return r;
}
class No3046Yukicoder {
public:

void solve(std::istream& cin, std::ostream& cout, std::ostream& cerr) {
    int k, n;
    cin >> k >> n;
    vector<int> v(n);
    for (auto &&i : v) {
        cin >> i;
    }
    vector<int> p(2e5+5, 0);
    for (int i = 0; i < n; ++i) {
        p[v[i]] = MOD-1;
    }
    p[0] = 1;
    poly pp(p);
    poly ppinv = inv(pp);
    cout << ppinv[k] << "\n";

}


};


#undef int
int main() {

	No3046Yukicoder solver;
	std::istream& in(std::cin);
	std::ostream& out(std::cout);
    std::ostringstream err;
	in.tie(0); ios::sync_with_stdio(0);
    solver.solve(in, out,err);
	return 0;
}
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