結果

問題 No.2747 Permutation Adjacent Sum
ユーザー noya2noya2
提出日時 2024-04-21 01:40:29
言語 C++23
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 252 ms / 3,000 ms
コード長 18,756 bytes
コンパイル時間 3,264 ms
コンパイル使用メモリ 259,208 KB
実行使用メモリ 32,740 KB
最終ジャッジ日時 2024-10-13 00:06:04
合計ジャッジ時間 9,862 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge2
このコードへのチャレンジ
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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 127 ms
13,876 KB
testcase_01 AC 55 ms
6,820 KB
testcase_02 AC 88 ms
12,308 KB
testcase_03 AC 35 ms
6,820 KB
testcase_04 AC 135 ms
18,112 KB
testcase_05 AC 252 ms
32,676 KB
testcase_06 AC 156 ms
18,424 KB
testcase_07 AC 127 ms
13,816 KB
testcase_08 AC 151 ms
20,516 KB
testcase_09 AC 251 ms
31,124 KB
testcase_10 AC 58 ms
8,884 KB
testcase_11 AC 106 ms
13,892 KB
testcase_12 AC 32 ms
6,816 KB
testcase_13 AC 57 ms
9,476 KB
testcase_14 AC 168 ms
19,652 KB
testcase_15 AC 221 ms
30,860 KB
testcase_16 AC 120 ms
14,036 KB
testcase_17 AC 199 ms
22,424 KB
testcase_18 AC 194 ms
21,996 KB
testcase_19 AC 24 ms
7,296 KB
testcase_20 AC 148 ms
18,088 KB
testcase_21 AC 190 ms
20,436 KB
testcase_22 AC 194 ms
21,020 KB
testcase_23 AC 89 ms
13,076 KB
testcase_24 AC 131 ms
13,352 KB
testcase_25 AC 96 ms
12,024 KB
testcase_26 AC 164 ms
19,788 KB
testcase_27 AC 163 ms
20,664 KB
testcase_28 AC 147 ms
20,304 KB
testcase_29 AC 108 ms
18,156 KB
testcase_30 AC 239 ms
32,740 KB
testcase_31 AC 243 ms
32,736 KB
testcase_32 AC 236 ms
32,736 KB
testcase_33 AC 250 ms
32,736 KB
testcase_34 AC 239 ms
32,736 KB
testcase_35 AC 6 ms
6,820 KB
testcase_36 AC 6 ms
6,820 KB
testcase_37 AC 5 ms
6,820 KB
testcase_38 AC 6 ms
6,816 KB
testcase_39 AC 6 ms
6,820 KB
testcase_40 AC 6 ms
6,820 KB
testcase_41 AC 6 ms
6,816 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 # 

#line 2 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"
using namespace std;

#include<bits/stdc++.h>
#line 1 "/Users/noya2/Desktop/Noya2_library/template/inout_old.hpp"
namespace noya2 {

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

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v){
    int s = (int)v.size();
    for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
    return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v){
    for (auto &x : v) is >> x;
    return is;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &...u){
    cin >> t;
    in(u...);
}

void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u){
    cout << t;
    if (sizeof...(u)) cout << sep;
    out(u...);
}

template<typename T>
void out(const vector<vector<T>> &vv){
    int s = (int)vv.size();
    for (int i = 0; i < s; i++) out(vv[i]);
}

struct IoSetup {
    IoSetup(){
        cin.tie(nullptr);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(15);
        cerr << fixed << setprecision(7);
    }
} iosetup_noya2;

} // namespace noya2
#line 1 "/Users/noya2/Desktop/Noya2_library/template/const.hpp"
namespace noya2{

const int iinf = 1'000'000'007;
const long long linf = 2'000'000'000'000'000'000LL;
const long long mod998 =  998244353;
const long long mod107 = 1000000007;
const long double pi = 3.14159265358979323;
const vector<int> dx = {0,1,0,-1,1,1,-1,-1};
const vector<int> dy = {1,0,-1,0,1,-1,-1,1};
const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const string alp = "abcdefghijklmnopqrstuvwxyz";
const string NUM = "0123456789";

void yes(){ cout << "Yes\n"; }
void no(){ cout << "No\n"; }
void YES(){ cout << "YES\n"; }
void NO(){ cout << "NO\n"; }
void yn(bool t){ t ? yes() : no(); }
void YN(bool t){ t ? YES() : NO(); }

} // namespace noya2
#line 1 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"
namespace noya2{

unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){
    if (a == 0 || b == 0) return a + b;
    int n = __builtin_ctzll(a); a >>= n;
    int m = __builtin_ctzll(b); b >>= m;
    while (a != b) {
        int mm = __builtin_ctzll(a - b);
        bool f = a > b;
        unsigned long long c = f ? a : b;
        b = f ? b : a;
        a = (c - b) >> mm;
    }
    return a << min(n, m);
}

template<typename T> T gcd_fast(T a, T b){ return static_cast<T>(inner_binary_gcd(abs(a),abs(b))); }

long long sqrt_fast(long long n) {
    if (n <= 0) return 0;
    long long x = sqrt(n);
    while ((x + 1) * (x + 1) <= n) x++;
    while (x * x > n) x--;
    return x;
}

template<typename T> T floor_div(const T n, const T d) {
    assert(d != 0);
    return n / d - static_cast<T>((n ^ d) < 0 && n % d != 0);
}

template<typename T> T ceil_div(const T n, const T d) {
    assert(d != 0);
    return n / d + static_cast<T>((n ^ d) >= 0 && n % d != 0);
}

template<typename T> void uniq(vector<T> &v){
    sort(v.begin(),v.end());
    v.erase(unique(v.begin(),v.end()),v.end());
}

template <typename T, typename U> inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; }

template <typename T, typename U> inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; }

template<typename T> inline bool range(T l, T x, T r){ return l <= x && x < r; }

} // namespace noya2
#line 8 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"

#define rep(i,n) for (int i = 0; i < (int)(n); i++)
#define repp(i,m,n) for (int i = (m); i < (int)(n); i++)
#define reb(i,n) for (int i = (int)(n-1); i >= 0; i--)
#define all(v) (v).begin(),(v).end()

using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
using pil = pair<int,ll>;
using pli = pair<ll,int>;

namespace noya2{

/*　~ (. _________ . /)　*/

}

using namespace noya2;


#line 2 "c.cpp"

#line 2 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp"

#line 2 "/Users/noya2/Desktop/Noya2_library/math/prime.hpp"

#line 4 "/Users/noya2/Desktop/Noya2_library/math/prime.hpp"

namespace noya2 {

constexpr ll safe_mod(ll x, ll m) {
    x %= m;
    if (x < 0) x += m;
    return x;
}

constexpr ll pow_mod_constexpr(ll x, ll n, int m) {
    if (m == 1) return 0;
    uint _m = (uint)(m);
    ull r = 1;
    ull y = safe_mod(x, m);
    while (n) {
        if (n & 1) r = (r * y) % _m;
        y = (y * y) % _m;
        n >>= 1;
    }
    return r;
}

constexpr bool is_prime_constexpr(int n) {
    if (n <= 1) return false;
    if (n == 2 || n == 7 || n == 61) return true;
    if (n % 2 == 0) return false;
    ll d = n - 1;
    while (d % 2 == 0) d /= 2;
    constexpr ll bases[3] = {2, 7, 61};
    for (ll a : bases) {
        ll t = d;
        ll y = pow_mod_constexpr(a, t, n);
        while (t != n - 1 && y != 1 && y != n - 1) {
            y = y * y % n;
            t <<= 1;
        }
        if (y != n - 1 && t % 2 == 0) {
            return false;
        }
    }
    return true;
}
template <int n> constexpr bool is_prime_flag = is_prime_constexpr(n);

constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
    a = safe_mod(a, b);
    if (a == 0) return {b, 0};
    long long s = b, t = a;
    long long m0 = 0, m1 = 1;
    while (t) {
        long long u = s / t;
        s -= t * u;
        m0 -= m1 * u; 
        auto tmp = s;
        s = t;
        t = tmp;
        tmp = m0;
        m0 = m1;
        m1 = tmp;
    }
    if (m0 < 0) m0 += b / s;
    return {s, m0};
}

constexpr int primitive_root_constexpr(int m) {
    if (m == 2) return 1;
    if (m == 167772161) return 3;
    if (m == 469762049) return 3;
    if (m == 754974721) return 11;
    if (m == 998244353) return 3;
    int divs[20] = {};
    divs[0] = 2;
    int cnt = 1;
    int x = (m - 1) / 2;
    while (x % 2 == 0) x /= 2;
    for (int i = 3; (ll)(i)*i <= x; i += 2) {
        if (x % i == 0) {
            divs[cnt++] = i;
            while (x % i == 0) {
                x /= i;
            }
        }
    }
    if (x > 1) {
        divs[cnt++] = x;
    }
    for (int g = 2;; g++) {
        bool ok = true;
        for (int i = 0; i < cnt; i++) {
            if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
                ok = false;
                break;
            }
        }
        if (ok) return g;
    }
}
template <int m> constexpr int primitive_root_flag = primitive_root_constexpr(m);

} // namespace noya2
#line 4 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp"

namespace noya2{

struct barrett {
    uint _m;
    ull  im;
    explicit barrett(uint m) : _m(m), im((ull)(-1) / m + 1) {}
    uint umod() const { return _m; }
    uint mul(uint a, uint b) const {
        ull z = a;
        z *= b;
        ull x = ull((__uint128_t(z) * im) >> 64);
        uint v = (uint)(z - x * _m);
        if (_m <= v) v += _m;
        return v;
    }
};

template <int m>
struct static_modint {
    using mint = static_modint;
  public:
    static constexpr int mod() { return m; }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }
    constexpr static_modint() : _v(0) {}
    template<signed_integral T>
    constexpr static_modint(T v){
        ll x = (ll)(v % (ll)(umod()));
        if (x < 0) x += umod();
        _v = (uint)(x);
    }
    template<unsigned_integral T>
    constexpr static_modint(T v){
        _v = (uint)(v % umod());
    }
    constexpr unsigned int val() const { return _v; }
    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }
    constexpr mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    constexpr mint& operator-=(const mint& rhs) {
        _v -= rhs._v;
        if (_v >= umod()) _v += umod();
        return *this;
    }
    constexpr mint& operator*=(const mint& rhs) {
        ull z = _v;
        z *= rhs._v;
        _v = (uint)(z % umod());
        return *this;
    }
    constexpr mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
    constexpr mint operator+() const { return *this; }
    constexpr mint operator-() const { return mint() - *this; }
    constexpr mint pow(ll n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    constexpr mint inv() const {
        if (prime) {
            assert(_v);
            return pow(umod() - 2);
        } else {
            auto eg = inv_gcd(_v, m);
            assert(eg.first == 1);
            return eg.second;
        }
    }
    friend constexpr mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend constexpr mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend constexpr mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend constexpr mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend constexpr bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend constexpr bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }
    friend std::ostream &operator<<(std::ostream &os, const mint& p) {
        return os << p.val();
    }
    friend std::istream &operator>>(std::istream &is, mint &a) {
        long long t; is >> t;
        a = mint(t);
        return (is);
    }

  private:
    unsigned int _v;
    static constexpr unsigned int umod() { return m; }
    static constexpr bool prime = is_prime_flag<m>;
};


template <int id> struct dynamic_modint {
    using mint = dynamic_modint;
  public:
    static int mod() { return (int)(bt.umod()); }
    static void set_mod(int m) {
        assert(1 <= m);
        bt = barrett(m);
    }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    dynamic_modint() : _v(0) {}
    template<signed_integral T>
    dynamic_modint(T v){
        ll x = (ll)(v % (ll)(mod()));
        if (x < 0) x += mod();
        _v = (uint)(x);
    }
    template<unsigned_integral T>
    dynamic_modint(T v){
        _v = (uint)(v % mod());
    }
    uint val() const { return _v; }
    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }
    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v += mod() - rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        _v = bt.mul(_v, rhs._v);
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }
    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        auto eg = noya2::inv_gcd(_v, mod());
        assert(eg.first == 1);
        return eg.second;
    }
    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }
    friend std::ostream &operator<<(std::ostream &os, const mint& p) {
        return os << p.val();
    }
    friend std::istream &operator>>(std::istream &is, mint &a) {
        long long t; is >> t;
        a = mint(t);
        return (is);
    }

  private:
    unsigned int _v;
    static barrett bt;
    static unsigned int umod() { return bt.umod(); }
};
template <int id> noya2::barrett dynamic_modint<id>::bt(998244353);

using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;

template<typename T>
concept Modint = requires (T &a){
    T::mod();
    a.inv();
    a.val();
    a.pow(declval<int>());
};

} // namespace noya2
#line 4 "c.cpp"
using mint = modint998244353;
#line 2 "/Users/noya2/Desktop/Noya2_library/math/binomial.hpp"

namespace noya2 {

template<typename mint>
struct binomial {
    binomial(int len = 300000){ extend(len); }
    static mint fact(int n){
        if (n < 0) return 0;
        while (n >= (int)_fact.size()) extend();
        return _fact[n];
    }
    static mint ifact(int n){
        if (n < 0) return 0;
        while (n >= (int)_fact.size()) extend();
        return _ifact[n];
    }
    static mint inv(int n){
        return ifact(n) * fact(n-1);
    }
    static mint C(int n, int r){
        if (!(0 <= r && r <= n)) return 0;
        return fact(n) * ifact(r) * ifact(n-r);
    }
    static mint P(int n, int r){
        if (!(0 <= r && r <= n)) return 0;
        return fact(n) * ifact(n-r);
    }
    inline mint operator()(int n, int r) { return C(n, r); }
    template<class... Cnts> static mint M(const Cnts&... cnts){
        return multinomial(0,1,cnts...);
    }
  private:
    static mint multinomial(const int& sum, const mint& div_prod){
        if (sum < 0) return 0;
        return fact(sum) * div_prod;
    }
    template<class... Tail> static mint multinomial(const int& sum, const mint& div_prod, const int& n1, const Tail&... tail){
        if (n1 < 0) return 0;
        return multinomial(sum+n1,div_prod*ifact(n1),tail...);
    }
    static vector<mint> _fact, _ifact;
    static void extend(int len = -1){
        if (_fact.empty()){
            _fact = _ifact = {1,1};
        }
        int siz = _fact.size();
        if (len == -1) len = siz * 2;
        len = min<int>(len, mint::mod()-1);
        if (len < siz) return ;
        _fact.resize(len+1), _ifact.resize(len+1);
        for (int i = siz; i <= len; i++) _fact[i] = _fact[i-1] * i;
        _ifact[len] = _fact[len].inv();
        for (int i = len; i > siz; i--) _ifact[i-1] = _ifact[i] * i;
    }
};
template<typename T>
std::vector<T>binomial<T>::_fact = vector<T>(2,T(1));
template<typename T>
std::vector<T>binomial<T>::_ifact = vector<T>(2,T(1));

} // namespace noya2
#line 6 "c.cpp"
binomial<mint> bnm;


/*


// given  : y(x=0) , y(x=1) , ... , y(k)
// return : y(x)
template <typename mint>
mint lagrange_interpolation(const vector<mint>& y, long long x,
                            Binomial<mint>& C) {
  int N = (int)y.size() - 1;
  if (x <= N) return y[x];
  mint ret = 0;
  vector<mint> dp(N + 1, 1), pd(N + 1, 1);
  mint a = x, one = 1;
  for (int i = 0; i < N; i++) dp[i + 1] = dp[i] * a, a -= one;
  for (int i = N; i > 0; i--) pd[i - 1] = pd[i] * a, a += one;
  for (int i = 0; i <= N; i++) {
    mint tmp = y[i] * dp[i] * pd[i] * C.finv(i) * C.finv(N - i);
    ret += ((N - i) & 1) ? -tmp : tmp;
  }
  return ret;
}

*/

mint lagrange_interpolation(const vector<mint> &y, mint x){
    if (x.val() < y.size()){
        return y[x.val()];
    }
    int n = y.size() - 1;
    vector<mint> lui(n+1,1), rui(n+1,1);
    mint a = x;
    rep(i,n){
        lui[i+1] = lui[i] * a;
        a -= 1;
    }
    reb(i,n){
        rui[i] = rui[i+1] * a;
        a += 1;
    }
    mint ans = 0;
    rep(i,n+1){
        mint tmp = y[i] * lui[i] * rui[i] * bnm.ifact(i) * bnm.ifact(n-i);
        ans += ((n-i) & 1) ? -tmp : tmp;
    }
    return ans;
}

// sum[0 <= i <= n] i^k
mint powsum(ll n, int k){
    vector<mint> y(k+2,0);
    rep(i,k+1){
        y[i+1] = y[i] + mint(i+1).pow(k);
    }
    return lagrange_interpolation(y,n);
}


const std::vector<int> fact_par1e7_mod998 = 
{

1 ,
295201906 ,
160030060 ,
957629942 ,
545208507 ,
213689172 ,
760025067 ,
939830261 ,
506268060 ,
39806322 ,
808258749 ,
440133909 ,
686156489 ,
741797144 ,
390377694 ,
12629586 ,
544711799 ,
104121967 ,
495867250 ,
421290700 ,
117153405 ,
57084755 ,
202713771 ,
675932866 ,
79781699 ,
956276337 ,
652678397 ,
35212756 ,
655645460 ,
468129309 ,
761699708 ,
533047427 ,
287671032 ,
206068022 ,
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};

const long long factpar = 10000000;

long long fact998(long long n){
    if (n >= mod998) return 0;
    long long res = fact_par1e7_mod998[n/factpar];
    for (ll nn = n/factpar*factpar+1; nn <= n; nn++){
        res = (res * nn) % mod998;
    }
    return res;
}

void solve(){
    int n, k; in(n,k);
    mint ans = n*powsum(n-1,k) - powsum(n-1,k+1);
    ans *= 2*fact998(n-1);
    out(ans);
}

int main(){
    int t = 1; //in(t);
    while (t--) { solve(); }
}
0