結果
| 問題 | No.665 Bernoulli Bernoulli |
| ユーザー |
 kacho65535
|
| 提出日時 | 2020-12-26 22:04:05 |
| 言語 | C++14 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 672 ms / 2,000 ms |
| コード長 | 29,359 bytes |
| コンパイル時間 | 1,949 ms |
| コンパイル使用メモリ | 183,944 KB |
| 実行使用メモリ | 26,904 KB |
| 最終ジャッジ日時 | 2024-09-25 02:12:27 |
| 合計ジャッジ時間 | 14,861 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge4 |
（要ログイン）
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 | 398 ms
26,736 KB |
| testcase_01 | AC | 397 ms
26,660 KB |
| testcase_02 | AC | 672 ms
26,796 KB |
| testcase_03 | AC | 672 ms
26,904 KB |
| testcase_04 | AC | 658 ms
26,876 KB |
| testcase_05 | AC | 638 ms
26,788 KB |
| testcase_06 | AC | 634 ms
26,684 KB |
| testcase_07 | AC | 628 ms
26,684 KB |
| testcase_08 | AC | 627 ms
26,796 KB |
| testcase_09 | AC | 660 ms
26,808 KB |
| testcase_10 | AC | 628 ms
26,836 KB |
| testcase_11 | AC | 666 ms
26,808 KB |
| testcase_12 | AC | 658 ms
26,836 KB |
| testcase_13 | AC | 669 ms
26,884 KB |
| testcase_14 | AC | 670 ms
26,820 KB |
| testcase_15 | AC | 634 ms
26,704 KB |
| testcase_16 | AC | 646 ms
26,664 KB |
| testcase_17 | AC | 637 ms
26,788 KB |
| testcase_18 | AC | 629 ms
26,800 KB |
ソースコード
#include <bits/stdc++.h>
#ifndef ATCODER_INTERNAL_BITOP_HPP
#define ATCODER_INTERNAL_BITOP_HPP 1
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder
{
namespace internal
{
// @param n `0 <= n`
// @return minimum non-negative `x` s.t. `n <= 2**x`
int ceil_pow2(int n)
{
int x = 0;
while ((1U << x) < (unsigned int)(n))
x++;
return x;
}
// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
int bsf(unsigned int n)
{
#ifdef _MSC_VER
unsigned long index;
_BitScanForward(&index, n);
return index;
#else
return __builtin_ctz(n);
#endif
}
} // namespace internal
} // namespace atcoder
#endif // ATCODER_INTERNAL_BITOP_HPP
#ifndef ATCODER_INTERNAL_MATH_HPP
#define ATCODER_INTERNAL_MATH_HPP 1
#include <utility>
namespace atcoder
{
namespace internal
{
// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m)
{
x %= m;
if (x < 0)
x += m;
return x;
}
// Fast moduler by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett
{
unsigned int _m;
unsigned long long im;
// @param m `1 <= m`
barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
// @return m
unsigned int umod() const { return _m; }
// @param a `0 <= a < m`
// @param b `0 <= b < m`
// @return `a * b % m`
unsigned int mul(unsigned int a, unsigned int b) const
{
// [1] m = 1
// a = b = im = 0, so okay
// [2] m >= 2
// im = ceil(2^64 / m)
// -> im * m = 2^64 + r (0 <= r < m)
// let z = a*b = c*m + d (0 <= c, d < m)
// a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
// c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2
// ((ab * im) >> 64) == c or c + 1
unsigned long long z = a;
z *= b;
#ifdef _MSC_VER
unsigned long long x;
_umul128(z, im, &x);
#else
unsigned long long x =
(unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
unsigned int v = (unsigned int)(z - x * _m);
if (_m <= v)
v += _m;
return v;
}
};
// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr long long pow_mod_constexpr(long long x, long long n, int m)
{
if (m == 1)
return 0;
unsigned int _m = (unsigned int)(m);
unsigned long long r = 1;
unsigned long long y = safe_mod(x, m);
while (n)
{
if (n & 1)
r = (r * y) % _m;
y = (y * y) % _m;
n >>= 1;
}
return r;
}
// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
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;
long long d = n - 1;
while (d % 2 == 0)
d /= 2;
for (long long a : {2, 7, 61})
{
long long t = d;
long long 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 = is_prime_constexpr(n);
// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
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};
// Contracts:
// [1] s - m0 * a = 0 (mod b)
// [2] t - m1 * a = 0 (mod b)
// [3] s * |m1| + t * |m0| <= b
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; // |m1 * u| <= |m1| * s <= b
// [3]:
// (s - t * u) * |m1| + t * |m0 - m1 * u|
// <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
// = s * |m1| + t * |m0| <= b
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
// by [3]: |m0| <= b/g
// by g != b: |m0| < b/g
if (m0 < 0)
m0 += b / s;
return {s, m0};
}
// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
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; (long long)(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 = primitive_root_constexpr(m);
} // namespace internal
} // namespace atcoder
#endif // ATCODER_INTERNAL_MATH_HPP
#ifndef ATCODER_INTERNAL_QUEUE_HPP
#define ATCODER_INTERNAL_QUEUE_HPP 1
#include <vector>
namespace atcoder
{
namespace internal
{
template <class T>
struct simple_queue
{
std::vector<T> payload;
int pos = 0;
void reserve(int n) { payload.reserve(n); }
int size() const { return int(payload.size()) - pos; }
bool empty() const { return pos == int(payload.size()); }
void push(const T &t) { payload.push_back(t); }
T &front() { return payload[pos]; }
void clear()
{
payload.clear();
pos = 0;
}
void pop() { pos++; }
};
} // namespace internal
} // namespace atcoder
#endif // ATCODER_INTERNAL_QUEUE_HPP
#ifndef ATCODER_INTERNAL_SCC_HPP
#define ATCODER_INTERNAL_SCC_HPP 1
#include <algorithm>
#include <utility>
#include <vector>
namespace atcoder
{
namespace internal
{
template <class E>
struct csr
{
std::vector<int> start;
std::vector<E> elist;
csr(int n, const std::vector<std::pair<int, E>> &edges)
: start(n + 1), elist(edges.size())
{
for (auto e : edges)
{
start[e.first + 1]++;
}
for (int i = 1; i <= n; i++)
{
start[i] += start[i - 1];
}
auto counter = start;
for (auto e : edges)
{
elist[counter[e.first]++] = e.second;
}
}
};
// Reference:
// R. Tarjan,
// Depth-First Search and Linear Graph Algorithms
struct scc_graph
{
public:
scc_graph(int n) : _n(n) {}
int num_vertices() { return _n; }
void add_edge(int from, int to) { edges.push_back({from, {to}}); }
// @return pair of (# of scc, scc id)
std::pair<int, std::vector<int>> scc_ids()
{
auto g = csr<edge>(_n, edges);
int now_ord = 0, group_num = 0;
std::vector<int> visited, low(_n), ord(_n, -1), ids(_n);
visited.reserve(_n);
auto dfs = [&](auto self, int v) -> void {
low[v] = ord[v] = now_ord++;
visited.push_back(v);
for (int i = g.start[v]; i < g.start[v + 1]; i++)
{
auto to = g.elist[i].to;
if (ord[to] == -1)
{
self(self, to);
low[v] = std::min(low[v], low[to]);
}
else
{
low[v] = std::min(low[v], ord[to]);
}
}
if (low[v] == ord[v])
{
while (true)
{
int u = visited.back();
visited.pop_back();
ord[u] = _n;
ids[u] = group_num;
if (u == v)
break;
}
group_num++;
}
};
for (int i = 0; i < _n; i++)
{
if (ord[i] == -1)
dfs(dfs, i);
}
for (auto &x : ids)
{
x = group_num - 1 - x;
}
return {group_num, ids};
}
std::vector<std::vector<int>> scc()
{
auto ids = scc_ids();
int group_num = ids.first;
std::vector<int> counts(group_num);
for (auto x : ids.second)
counts[x]++;
std::vector<std::vector<int>> groups(ids.first);
for (int i = 0; i < group_num; i++)
{
groups[i].reserve(counts[i]);
}
for (int i = 0; i < _n; i++)
{
groups[ids.second[i]].push_back(i);
}
return groups;
}
private:
int _n;
struct edge
{
int to;
};
std::vector<std::pair<int, edge>> edges;
};
} // namespace internal
} // namespace atcoder
#endif // ATCODER_INTERNAL_SCC_HPP
#ifndef ATCODER_INTERNAL_TYPE_TRAITS_HPP
#define ATCODER_INTERNAL_TYPE_TRAITS_HPP 1
#include <cassert>
#include <numeric>
#include <type_traits>
namespace atcoder
{
namespace internal
{
#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value ||
std::is_same<T, __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int128 =
typename std::conditional<std::is_same<T, __uint128_t>::value ||
std::is_same<T, unsigned __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using make_unsigned_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value,
__uint128_t,
unsigned __int128>;
template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
is_signed_int128<T>::value ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
std::is_signed<T>::value) ||
is_signed_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<(is_integral<T>::value &&
std::is_unsigned<T>::value) ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<
is_signed_int128<T>::value,
make_unsigned_int128<T>,
typename std::conditional<std::is_signed<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type>::type;
#else
template <class T>
using is_integral = typename std::is_integral<T>;
template <class T>
using is_signed_int =
typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<is_integral<T>::value &&
std::is_unsigned<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type;
#endif
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T>
using to_unsigned_t = typename to_unsigned<T>::type;
} // namespace internal
} // namespace atcoder
#endif // ATCODER_INTERNAL_TYPE_TRAITS_HPP
#ifndef ATCODER_MODINT_HPP
#define ATCODER_MODINT_HPP 1
#include <cassert>
#include <numeric>
#include <type_traits>
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder
{
namespace internal
{
struct modint_base
{
};
struct static_modint_base : modint_base
{
};
template <class T>
using is_modint = std::is_base_of<modint_base, T>;
template <class T>
using is_modint_t = std::enable_if_t<is_modint<T>::value>;
} // namespace internal
template <int m, std::enable_if_t<(1 <= m)> * = nullptr>
struct static_modint : internal::static_modint_base
{
using mint = static_modint;
public:
static constexpr int mod() { return m; }
static mint raw(int v)
{
mint x;
x._v = v;
return x;
}
static_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T> * = nullptr>
static_modint(T v)
{
long long x = (long long)(v % (long long)(umod()));
if (x < 0)
x += umod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T> * = nullptr>
static_modint(T v)
{
_v = (unsigned int)(v % umod());
}
static_modint(bool v) { _v = ((unsigned int)(v) % umod()); }
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;
}
mint &operator+=(const mint &rhs)
{
_v += rhs._v;
if (_v >= umod())
_v -= umod();
return *this;
}
mint &operator-=(const mint &rhs)
{
_v -= rhs._v;
if (_v >= umod())
_v += umod();
return *this;
}
mint &operator*=(const mint &rhs)
{
unsigned long long z = _v;
z *= rhs._v;
_v = (unsigned int)(z % umod());
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
{
if (prime)
{
assert(_v);
return pow(umod() - 2);
}
else
{
auto eg = internal::inv_gcd(_v, m);
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;
}
private:
unsigned int _v;
static constexpr unsigned int umod() { return m; }
static constexpr bool prime = internal::is_prime<m>;
};
template <int id>
struct dynamic_modint : internal::modint_base
{
using mint = dynamic_modint;
public:
static int mod() { return (int)(bt.umod()); }
static void set_mod(int m)
{
assert(1 <= m);
bt = internal::barrett(m);
}
static mint raw(int v)
{
mint x;
x._v = v;
return x;
}
dynamic_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T> * = nullptr>
dynamic_modint(T v)
{
long long x = (long long)(v % (long long)(mod()));
if (x < 0)
x += mod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T> * = nullptr>
dynamic_modint(T v)
{
_v = (unsigned int)(v % mod());
}
dynamic_modint(bool v) { _v = ((unsigned int)(v) % mod()); }
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;
}
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 = internal::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;
}
private:
unsigned int _v;
static internal::barrett bt;
static unsigned int umod() { return bt.umod(); }
};
template <int id>
internal::barrett dynamic_modint<id>::bt = 998244353;
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
namespace internal
{
template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;
template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;
template <class>
struct is_dynamic_modint : public std::false_type
{
};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type
{
};
template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;
} // namespace internal
} // namespace atcoder
#endif // ATCODER_MODINT_HPP
#pragma GCC optimize("Ofast")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("avx")
#include <bits/stdc++.h>
#define _GLIBCXX_DEBUG
using namespace std;
using namespace atcoder;
using ll = long long;
using vec = vector<ll>;
using vect = vector<double>;
using Graph = vector<vector<ll>>;
#define endl '\n'
#define loop(i, n) for (register int i = 0; i < n; i++)
#define Loop(i, m, n) for (int i = m; i < n; i++)
#define pool(i, n) for (int i = n; i >= 0; i--)
#define Pool(i, m, n) for (int i = n; i >= m; i--)
#define modd 1000000007ll
//#define modd 998244353ll
#define flagcount(bit) __builtin_popcount(bit)
#define flag(x) (1ll << x)
#define flagadd(bit, x) bit |= flag(x)
#define flagpop(bit, x) bit &= ~flag(x)
#define flagon(bit, i) bit &flag(i)
#define flagoff(bit, i) !(bit & (1ll << i))
#define all(v) v.begin(), v.end()
#define low2way(v, x) lower_bound(all(v), x)
#define high2way(v, x) upper_bound(all(v), x)
#define idx_lower(v, x) (distance(v.begin(), low2way(v, x))) //配列vでx未満の要素数を返す
#define idx_upper(v, x) (distance(v.begin(), high2way(v, x))) //配列vでx以下の要素数を返す
#define idx_lower2(v, x) (v.size() - idx_lower(v, x)) //配列vでx以上の要素数を返す
#define idx_upper2(v, x) (v.size() - idx_upper(v, x)) //配列vでxより大きい要素の数を返す
#define putout(a) cout << a << '\n'
#define Sum(v) accumulate(all(v), 0ll)
ll ctoi(char c)
{
if (c >= '0' && c <= '9')
{
return c - '0';
}
return -1;
}
template <typename T>
string make_string(T N)
{
string ret;
T now = N;
while (now > 0)
{
T x = now % 10;
ret += (char)('0' + x);
now /= 10;
}
reverse(all(ret));
return ret;
}
template <typename T>
T gcd(T a, T b)
{
if (a % b == 0)
{
return (b);
}
else
{
return (gcd(b, a % b));
}
}
template <typename T>
T lcm(T x, T y)
{
T z = gcd(x, y);
return x * y / z;
}
template <typename T>
bool primejudge(T n)
{
if (n < 2)
return false;
else if (n == 2)
return true;
else if (n % 2 == 0)
return false;
double sqrtn = sqrt(n);
for (T i = 3; i < sqrtn + 1; i++)
{
if (n % i == 0)
{
return false;
}
i++;
}
return true;
}
template <typename T>
bool chmax(T &a, const T &b)
{
if (a < b)
{
a = b; // aをbで更新
return true;
}
return false;
}
template <typename T>
bool chmin(T &a, const T &b)
{
if (a > b)
{
a = b; // aをbで更新
return true;
}
return false;
}
//場合によって使い分ける
//const ll dx[4]={1,0,-1,0};
//const ll dy[4]={0,1,0,-1};
const ll dx[8] = {1, 1, 0, -1, -1, -1, 0, 1};
const ll dy[8] = {0, 1, 1, 1, 0, -1, -1, -1};
//cout << fixed << setprecision(10);
//vector<vector<ll>> field(h, vector<ll>(w));
using mint = modint1000000007;
mint modpow(mint a, long long n)
{
mint res = 1;
while (n > 0)
{
if (n & 1)
res = res * a;
a *= a;
n >>= 1;
}
return res;
}
mint modinv(mint a)
{
return modpow(a, modd - 2);
}
vector<mint> fact(3000001); //fact[i]=(i!)
vector<mint> factinv(3000001); //factinv[i]=(i!)^-1
void COMinit()
{
mint now = 1;
fact[0] = 1;
factinv[0] = modinv(0);
for (long long i = 1; i < 3000001; i++)
{
now *= i;
fact[i] = now;
factinv[i] = modinv(now);
}
}
mint COM(long long n, long long r)
{
if (n < r)
return 0;
if (n < 0 || r < 0)
return 0;
if (n == r)
return 1;
if (r == 0)
return 1;
mint ans = fact[n];
ans *= factinv[r];
ans *= factinv[n - r];
return ans;
}
//1^K+2^K+...+N^Kを求める
mint Faulhaber(ll N, ll K)
{
N++;
vector<mint> B(K + 1, -1);
B[0] = 1;
for (ll i = 1; i <= K; i++)
{
B[i] *= modinv(i + 1);
mint S = 0;
for (ll k = 0; k <= i - 1; k++)
{
mint x = COM(1 + i, k);
x *= B[k];
S += x;
}
B[i] *= S;
}
vector<mint> pown(K + 2);
pown[0] = 1;
loop(i, K + 1) pown[i + 1] = pown[i] * N;
mint ans = modinv(K + 1);
mint SUM = 0;
for (ll i = 0; i <= K; i++)
{
mint x = COM(K + 1, i);
x *= B[i];
x *= pown[K + 1 - i];
SUM += x;
}
ans *= SUM;
return ans;
}
int main()
{
COMinit();
ll N, K;
cin >> N >> K;
mint ANS = Faulhaber(N, K);
putout(ANS.val());
return 0;
}