結果

問題 No.665 Bernoulli Bernoulli
ユーザー rniyarniya
提出日時 2021-09-21 15:23:35
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 3 ms / 2,000 ms
コード長 9,449 bytes
コンパイル時間 2,030 ms
コンパイル使用メモリ 206,788 KB
実行使用メモリ 6,944 KB
最終ジャッジ日時 2024-07-03 23:30:58
合計ジャッジ時間 2,817 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge1
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 2 ms
6,812 KB
testcase_01 AC 2 ms
6,940 KB
testcase_02 AC 2 ms
6,940 KB
testcase_03 AC 3 ms
6,940 KB
testcase_04 AC 3 ms
6,944 KB
testcase_05 AC 3 ms
6,940 KB
testcase_06 AC 3 ms
6,944 KB
testcase_07 AC 2 ms
6,940 KB
testcase_08 AC 3 ms
6,940 KB
testcase_09 AC 3 ms
6,944 KB
testcase_10 AC 3 ms
6,944 KB
testcase_11 AC 3 ms
6,940 KB
testcase_12 AC 3 ms
6,944 KB
testcase_13 AC 2 ms
6,944 KB
testcase_14 AC 3 ms
6,940 KB
testcase_15 AC 2 ms
6,940 KB
testcase_16 AC 2 ms
6,940 KB
testcase_17 AC 3 ms
6,940 KB
testcase_18 AC 3 ms
6,940 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 # 

#define LOCAL
#include <bits/stdc++.h>
using namespace std;
#pragma region Macros
typedef long long ll;
typedef __int128_t i128;
typedef unsigned int uint;
typedef unsigned long long ull;
#define ALL(x) (x).begin(), (x).end()

template <typename T> istream& operator>>(istream& is, vector<T>& v) {
    for (T& x : v) is >> x;
    return is;
}
template <typename T> ostream& operator<<(ostream& os, const vector<T>& v) {
    for (int i = 0; i < (int)v.size(); i++) {
        os << v[i] << (i + 1 == (int)v.size() ? "" : " ");
    }
    return os;
}
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> ostream& operator<<(ostream& os, const map<T, U>& m) {
    os << '{';
    for (auto itr = m.begin(); itr != m.end();) {
        os << '(' << itr->first << ',' << itr->second << ')';
        if (++itr != m.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const unordered_map<T, U>& m) {
    os << '{';
    for (auto itr = m.begin(); itr != m.end();) {
        os << '(' << itr->first << ',' << itr->second << ')';
        if (++itr != m.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const set<T>& s) {
    os << '{';
    for (auto itr = s.begin(); itr != s.end();) {
        os << *itr;
        if (++itr != s.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const multiset<T>& s) {
    os << '{';
    for (auto itr = s.begin(); itr != s.end();) {
        os << *itr;
        if (++itr != s.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const unordered_set<T>& s) {
    os << '{';
    for (auto itr = s.begin(); itr != s.end();) {
        os << *itr;
        if (++itr != s.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const deque<T>& v) {
    for (int i = 0; i < (int)v.size(); i++) {
        os << v[i] << (i + 1 == (int)v.size() ? "" : " ");
    }
    return os;
}

template <int i, typename T> void print_tuple(ostream&, const T&) {}
template <int i, typename T, typename H, class... Args> void print_tuple(ostream& os, const T& t) {
    if (i) os << ',';
    os << get<i>(t);
    print_tuple<i + 1, T, Args...>(os, t);
}
template <typename... Args> ostream& operator<<(ostream& os, const tuple<Args...>& t) {
    os << '{';
    print_tuple<0, tuple<Args...>, Args...>(os, t);
    return os << '}';
}

void debug_out() { cerr << '\n'; }
template <class Head, class... Tail> void debug_out(Head&& head, Tail&&... tail) {
    cerr << head;
    if (sizeof...(Tail) > 0) cerr << ", ";
    debug_out(move(tail)...);
}
#ifdef LOCAL
#define debug(...)                                                                   \
    cerr << " ";                                                                     \
    cerr << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]" << '\n'; \
    cerr << " ";                                                                     \
    debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif

template <typename T> T gcd(T x, T y) { return y != 0 ? gcd(y, x % y) : x; }
template <typename T> T lcm(T x, T y) { return x / gcd(x, y) * y; }

int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
int topbit(long long t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
int botbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); }
int botbit(long long a) { return a == 0 ? 64 : __builtin_ctzll(a); }
int popcount(signed t) { return __builtin_popcount(t); }
int popcount(long long t) { return __builtin_popcountll(t); }
bool ispow2(int i) { return i && (i & -i) == i; }

template <class T> T ceil(T x, T y) {
    assert(y >= 1);
    return (x > 0 ? (x + y - 1) / y : x / y);
}
template <class T> T floor(T x, T y) {
    assert(y >= 1);
    return (x > 0 ? x / y : (x - y + 1) / y);
}

template <class T1, class T2> inline bool chmin(T1& a, T2 b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}
template <class T1, class T2> inline bool chmax(T1& a, T2 b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}
#pragma endregion

#include <cassert>
#include <cstdint>
#include <iostream>

template <uint64_t Modulus> class modint {
    using i64 = int64_t;
    using u32 = uint32_t;
    using u64 = uint64_t;

    static_assert(Modulus < static_cast<uint32_t>(1) << 31, "Modulus must be less than 2**31");
    static constexpr u32 mod = Modulus;
    u32 v;

public:
    constexpr modint(const i64 x = 0) noexcept : v(x < 0 ? mod - 1 - (-(x + 1) % mod) : x % mod) {}
    constexpr u32& value() noexcept { return v; }
    constexpr const u32& value() const noexcept { return v; }
    constexpr modint operator+(const modint& rhs) const noexcept { return modint(*this) += rhs; }
    constexpr modint operator-(const modint& rhs) const noexcept { return modint(*this) -= rhs; }
    constexpr modint operator*(const modint& rhs) const noexcept { return modint(*this) *= rhs; }
    constexpr modint operator/(const modint& rhs) const noexcept { return modint(*this) /= rhs; }
    constexpr modint& operator+=(const modint& rhs) noexcept {
        v += rhs.v;
        if (v >= mod) v -= mod;
        return *this;
    }
    constexpr modint& operator-=(const modint& rhs) noexcept {
        if (v < rhs.v) v += mod;
        v -= rhs.v;
        return *this;
    }
    constexpr modint& operator*=(const modint& rhs) noexcept {
        v = (u64)v * rhs.v % mod;
        return *this;
    }
    constexpr modint& operator/=(const modint& rhs) noexcept { return *this *= rhs.inv(); }
    constexpr modint pow(long long n) const noexcept {
        assert(0 <= n);
        modint self(*this), res(1);
        while (n > 0) {
            if (n & 1) res *= self;
            self *= self;
            n >>= 1;
        }
        return res;
    }
    constexpr modint inv() const noexcept {
        assert(*this != 0);
        return pow(mod - 2);
    }
    constexpr modint& operator++() noexcept {
        if (++v == mod) v = 0;
        return *this;
    }
    constexpr modint& operator--() noexcept {
        if (v == 0) v = mod;
        return --v, *this;
    }
    constexpr modint operator++(int) noexcept {
        modint t = *this;
        return ++*this, t;
    }
    constexpr modint operator--(int) noexcept {
        modint t = *this;
        return --*this, t;
    }
    constexpr modint operator-() const noexcept { return modint(mod - v); }
    template <class T> friend constexpr modint operator+(T x, modint y) noexcept { return modint(x) + y; }
    template <class T> friend constexpr modint operator-(T x, modint y) noexcept { return modint(x) - y; }
    template <class T> friend constexpr modint operator*(T x, modint y) noexcept { return modint(x) * y; }
    template <class T> friend constexpr modint operator/(T x, modint y) noexcept { return modint(x) / y; }
    constexpr bool operator==(const modint& rhs) const noexcept { return v == rhs.v; }
    constexpr bool operator!=(const modint& rhs) const noexcept { return v != rhs.v; }
    constexpr bool operator!() const noexcept { return !v; }
    friend std::istream& operator>>(std::istream& s, modint& rhs) noexcept {
        i64 v;
        rhs = modint{(s >> v, v)};
        return s;
    }
    friend std::ostream& operator<<(std::ostream& s, const modint& rhs) noexcept { return s << rhs.v; }
};

/**
 * @brief modint
 * @docs docs/modulo/modint.md
 */

/**
 * @brief ラグランジュ補間
 * @docs docs/polynomial/lagrange_interpolation.md
 */
template <typename M> M lagrange_interpolation(vector<M> x, vector<M> y, M T) {
    int n = x.size() - 1;
    M res = 0;
    for (int i = 0; i <= n; i++) {
        M c = 1;
        for (int j = 0; j <= n; j++) {
            if (i == j) continue;
            (c *= T - x[j]) /= x[i] - x[j];
        }
        res += c * y[i];
    }
    return res;
}

template <typename M> M lagrange_interpolation_arithmetic(vector<M>& y, M T) {
    int n = y.size() - 1;
    if (T.value() <= n) return y[T.value()];
    vector<M> left(n + 1, 1), right(n + 1, 1), fac(n + 1, 1), finv(n + 1, 1);
    for (int i = 0; i < n; i++) left[i + 1] = left[i] * (T - i);
    for (int i = n - 1; i >= 0; --i) right[i] = right[i + 1] * (T - (i + 1));
    for (int i = 1; i <= n; i++) fac[i] = fac[i - 1] * i;
    finv[n] = (M)1 / fac[n];
    for (int i = n; i > 0; --i) finv[i - 1] = finv[i] * i;
    M res = 0;
    for (int i = 0; i <= n; i++) {
        M add = y[i] * left[i] * right[i] * finv[i] * finv[n - i];
        if ((n - i) & 1)
            res -= add;
        else
            res += add;
    }
    return res;
}

const int INF = 1e9;
const long long IINF = 1e18;
const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
const char dir[4] = {'D', 'R', 'U', 'L'};
const long long MOD = 1000000007;
// const long long MOD = 998244353;

using mint = modint<1000000007>;

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    long long n;
    int k;
    cin >> n >> k;
    vector<mint> A(k + 2, 0);
    for (int i = 1; i <= k + 1; i++) A[i] = A[i - 1] + ((mint)i).pow(k);
    cout << lagrange_interpolation_arithmetic(A, (mint)n) << '\n';
    return 0;
}
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