CodeChef July 18 E brute-force solution

main.cpp

#include <bits/stdc++.h>

using namespace std;
#define pb push_back
#define eb emplace_back
#define all(x) x.begin(), x.end()
#define debug(x) cerr << #x <<": " << (x) << endl
//在每个函数的入口处执行一次，出口处执行一次。然后就可以快速得知是哪个地方段错误了
#define DEBUG printf("Passing [%s] in LINE %d\n",__FUNCTION__,__LINE__)
#ifdef LOCAL
#define see(x) cout  << #x << ": " << (x) << endl

#endif
#ifndef LOCAL
#define see(x)
#endif

#define RED     "\033[31m"
#define RESET "\033[0m"
#define alert(x) cerr << RED << x << RESET << endl
#ifndef LOCAL
#define see(x)
#endif

#define rep(n) for(int _ = 0; _ != (n); ++_)
//#define rep(i, a, b) for(int i = (a); i <= (b); ++i)
#define Rng(i, n) for(int i = 0; i != (n); ++i)
#define rng(i, a, b) for(int i = (a); i < (b); ++i)
#define RNG(i, a) for(auto &i: (a))
#define dwn(i, r, l) for(int i = (r); i>=(l); i--)

namespace std {
    template<class T>
    T begin(std::pair<T, T> p)
    {
        return p.first;
    }
    template<class T>
    T end(std::pair<T, T> p)
    {
        return p.second;
    }
}


#if __cplusplus < 201402L
template<class Iterator>
std::reverse_iterator<Iterator> make_reverse_iterator(Iterator it)
{
    return std::reverse_iterator<Iterator>(it);
}
#endif

template<class Range>
std::pair<std::reverse_iterator<decltype(begin(std::declval<Range>()))>, std::reverse_iterator<decltype(begin(std::declval<Range>()))>> make_reverse_range(Range &&r)
{
    return std::make_pair(make_reverse_iterator(::begin(r)), make_reverse_iterator(::end(r)));
}

#define RRNG(x, cont) for (auto &x: make_reverse_range(cont))



template<class T> int sign(const T &a) { return a == 0 ? 0 : a > 0 ? 1 : -1; }
template<class T> inline T min(T a, T b, T c){return min(min(a, b), c);}
template<class T> inline T max(T a, T b, T c){return max(max(a, b), c);}
template<class T> void Min(T &a, const T &b){ a = min(a, b); }
template<class T> void Max(T &a, const T &b){ a = max(a, b); }

template<typename T> void println(const T &t) { cout << t << '\n'; }
template<typename T, typename ...Args> void println(const T &t, const Args &...rest) { cout << t << ' '; println(rest...); }

template<typename T> void print(const T &t) { cout << t << ' '; }

template<typename T, typename ...Args> void print(const T &t, const Args &...rest) { cout << t; print(rest...); }

// this overload is chosen when there's only one argument
template<class T> void scan(T &t) { cin >> t; }
template<class T, class ...Args> void scan(T &a, Args &...rest) { cin >> a; scan(rest...); }

using ll = long long;
using ull = unsigned long long;
using vec = vector<ll>;
using mat = vector<vec>;
using pii = pair<int, int>;
using pdd = pair<double, double>;
using pip = pair<int, pii>;
using szt = size_t;
using vi = vector<int>;
using vl = vector<ll>;
using vb = vector<bool>;
using vpii = vector<pii>;
using vvi = vector<vi>;
using pli = pair<ll,int>;

int cas;
const double pi = acos(-1);
ll mod = 1e9 + 7;

template<class T>
inline void add_mod(T &a, const T &b) {
    a += b;
    if (a >= mod) a -= mod;
}
template<class T>
void sub_mod(T &a, const T &b){
    a -= b;
    if (a < 0) a += mod;
}
auto bo=[](int x){ //二进制输出
    bitset<5> a(x);
    cout << a << endl;
};



mat operator*(const mat &a, const mat &b) {
    mat c(a.size(), vec(b[0].size()));
    for (int i = 0; i < a.size(); i++) {
        for (int j = 0; j < a[0].size(); j++) {
            if (a[i][j]) { // optimization for sparse matrix
                for (int k = 0; k < b[0].size(); k++) {
                    add_mod(c[i][k], a[i][j] * b[j][k] % mod);
                }
            }
        }
    }
    return c;
}

vec operator*(const mat &a, const vec &b) {
    vec c(a.size());
    for (int i = 0; i < a.size(); i++) {
        for (int j = 0; j < a[0].size(); j++) {
            add_mod(c[i], a[i][j] * b[j] % mod);
        }
    }
    return c;
}

mat pow(mat a, ull n) {
    mat res(a.size(), vec(a[0].size()));
    for (int i = 0; i < a.size(); i++) {
        res[i][i] = 1;
    }
    while (n) {
        if (n & 1) {
            res = res * a;
        }
        a = a * a;
        n >>= 1;
    }
    return res;
}

std::ostream& operator<<(std::ostream& os, __int128 T) {
    if (T<0) os<<"-";
    if (T>=10 ) os<<T/10;
    if (T<=-10) os<<(-(T/10));
    return os<<( (int) (T%10) >0 ? (int) (T%10) : -(int) (T%10) ) ;
}

__int128 LPOW(__int128 x, ll n) {
    __int128 res = 1;
    for (; n; n /= 2, x *= x, x %= mod) {
        if (n & 1) {
            res *= x;
            res %= mod;
        }
    }
    return res;
}

ll POW(ll x, ll n){
    ll res = 1;
    for (; n; n /= 2, x *= x, x %= mod) {
        if (n & 1) {
            res *= x;
            res %= mod;
        }
    }
    return res;
}


ll INV(ll x) {
    return POW(x, mod - 2);
}

ll inv(ll x){
//    see(x);
    return x == 1? 1: (mod - mod/x * inv(mod%x) % mod);
}



// 2D rotation
void rotate(double &x, double &y, double theta) {
    double tx = cos(theta) * x - sin(theta) * y;
    double ty = sin(theta) * x + cos(theta) * y;
    x = tx, y = ty;
}
namespace bit {
    const int BIT_N = 1e5 + 5;

    int bit[BIT_N];

    int sum(int x) {
        int res = 0;
        while (x) {
            res += bit[x];
            x -= x & -x;
        }
        return res;
    }

    int sum(int l, int r) {
        if (l > r) return 0;
        return sum(r) - sum(l - 1);
    }

    void add(int x, int v, int n) {
        while (x <= n) {
            bit[x] += v;
            x += x & -x;
        }
    }
}

namespace util{
    int len(ll x){return snprintf(nullptr, 0, "%lld", x);}
    vi get_d(ll x){
        vi res;
        while(x) {
            res.pb(x%10);
            x /= 10;
        }
        reverse(all(res));
        return res;
    }
    template <class T> T parity(const T &a){
        return a & 1;
    }
    template <class T>
    void out (const vector<T> &a){
        std::copy(a.begin(), a.end(), std::ostream_iterator<T>(std::cout, ", "));
        cout << endl;
    };
}

using namespace util;

// #include <ext/pb_ds/priority_queue.hpp>

// typedef __gnu_pbds :: priority_queue<pip, less<pip>, __gnu_pbds::thin_heap_tag > Heap;

// Heap h;

// Heap::point_iterator pos[N][N];
const ll LINF = LLONG_MAX/10;
const int INF = INT_MAX/10;
const int M = 3000 + 5;


const int N = 3e5+5;




int main() {
    // Single Cut of Failure taught me
    cout << std::fixed; // 使所有实数（默认）输出6位小数，即使实际小数位数多于6位。
    cout << setprecision(10);
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
#ifdef LOCAL
    freopen("main.in", "r", stdin);
//    freopen("main.out", "w", stdout);
#endif

    vl inv(3e5+5);
    vl fact(3e5+5);
    fact[0] = 1;
    rng(i, 1, fact.size()) fact[i] = (i * fact[i-1]) % mod;

    inv[1] = 1;
    rng(i, 2, inv.size()) {
        inv[i] = mod - mod/i*inv[mod%i] % mod;
    }

    int T = 1;
//    scan(T);
    while(T--) {
        int n;
        scan(n);
//        see(n);
        if(n <= 2) println(0);
        else{
            using poly = vl; // 多项式
            auto eval = [](const poly & a, ll x){
                ll res = 0;
                dwn(i, a.size()-1, 0) {
                    res *= x;
                    res %= mod;
                    add_mod(res, a[i]); // 保证 0<=res<mod, 0<=a[i]<= mod
                }
                return res;
            };
            auto integral = [&inv, &eval](poly &a){
                a.pb(0);
                dwn(i, a.size()-2, 0){
                    a[i+1] =  a[i] * inv[i+1] % mod;
                }
                a[0] = 0;
                add_mod(a[0], mod - eval(a, inv[2]));
            };

            poly a = {1, mod-1};

            rng(i, 3, n+1) {
                integral(a); // 积分之后，a是i-1次多项式
                ll t1 = mod - inv[2], t2 = mod - 2;
                ll fm = ::inv(fact[i-1]);
                ll comb = POW(t1, i-1) * fm % mod; // (-1/2)^{n-1} 除以分母 (i-1)!
                rng(j, 0, i){
                    add_mod(a[j], mod - comb);
                    // comb(i-1, j) x^j
                    // comb(i-1, j+1) = comb(i-1, j) * (i - 1 - j) / (j + 1);
                    comb *= (i - 1 - j) * inv[j+1] % mod * t2 % mod;
                    comb %= mod;
                }
                add_mod(a[0],  POW(inv[2], i - 1) * fm % mod);
            }  
            ll ans = 0;
            RNG(x, a){
                add_mod(ans, x);
            }
            if(ans < 0) ans += mod;
            println(ans * fact[n-1] % mod);
        }
    }

#ifdef LOCAL
    cerr << "Time elapsed: " << 1.0 * clock() / CLOCKS_PER_SEC << " s.\n";
#endif
    return 0;
}