提出 #29614471

---

ソースコード 拡げる

#include <bits/stdc++.h>
#include <cassert>
typedef long long int ll;
using namespace std;
// #include <atcoder/all>
// using namespace atcoder;
#define REP2(i, a, b) for (ll i = (a); i < (b); i++)
#define REP2R(i, a, b) for (ll i = (a); i >= (b); i--)
#define REP(i, b) REP2(i, 0, b)
#define ALL(coll) (coll).begin(), (coll).end()
#define SIZE(v) ((ll)((v).size()))

// @@ !! LIM(mod debug)

// ---- inserted library file algOp.cc

// Common definitions
//    zero, one, inverse

template<typename T>
constexpr T zero(const T& t) {
  if constexpr (is_integral_v<T> || is_floating_point_v<T>) { return (T)0; }
  else { return t.zero(); }
}

template<typename T>
constexpr T one(const T& t) {
  if constexpr (is_integral_v<T> || is_floating_point_v<T>) { return (T)1; }
  else { return t.one(); }
}

template<typename T>
constexpr T inverse(const T& t) {
  if constexpr (is_floating_point_v<T>) { return 1.0 / t; }
  else { return t.inverse(); }
}

// begin -- detection ideom
//    cf. https://blog.tartanllama.xyz/detection-idiom/

namespace detail {
  template <template <class...> class Trait, class Enabler, class... Args>
  struct is_detected : false_type{};

  template <template <class...> class Trait, class... Args>
  struct is_detected<Trait, void_t<Trait<Args...>>, Args...> : true_type{};
}

template <template <class...> class Trait, class... Args>
using is_detected = typename detail::is_detected<Trait, void, Args...>::type;

// end -- detection ideom


template<typename T>
// using subst_add_t = decltype(T::subst_add(declval<typename T::value_type &>(), declval<typename T::value_type>()));
using subst_add_t = decltype(T::subst_add);
template<typename T>
using has_subst_add = is_detected<subst_add_t, T>;

template<typename T>
using add_t = decltype(T::add);
template<typename T>
using has_add = is_detected<add_t, T>;

template<typename T>
using subst_mult_t = decltype(T::subst_mult);
template<typename T>
using has_subst_mult = is_detected<subst_mult_t, T>;

template<typename T>
using mult_t = decltype(T::mult);
template<typename T>
using has_mult = is_detected<mult_t, T>;

template<typename T>
using subst_subt_t = decltype(T::subst_subt);
template<typename T>
using has_subst_subt = is_detected<subst_subt_t, T>;

template<typename T>
using subt_t = decltype(T::subt);
template<typename T>
using has_subt = is_detected<subt_t, T>;

template <typename Opdef>
struct MyAlg {
  using T = typename Opdef::value_type;
  using value_type = T;
  T v;
  MyAlg() {}
  MyAlg(const T& v_) : v(v_) {}
  MyAlg(T&& v_) : v(move(v_)) {}
  bool operator==(MyAlg o) const { return v == o.v; }
  bool operator!=(MyAlg o) const { return v != o.v; }
  operator T() const { return v; }
  MyAlg zero() const { return MyAlg(Opdef::zero(v)); }
  MyAlg one() const { return MyAlg(Opdef::one(v)); }
  MyAlg inverse() const { return MyAlg(Opdef::inverse(v)); }
  MyAlg operator/=(const MyAlg& o) { return *this *= o.inverse(); }
  MyAlg operator/(const MyAlg& o) const { return (*this) * o.inverse(); }
  MyAlg operator-() const { return zero() - *this; }

  MyAlg& operator +=(const MyAlg& o) { 
    if constexpr (has_subst_add<Opdef>::value) {
      Opdef::subst_add(v, o.v);
      return *this;
    }else if constexpr (has_add<Opdef>::value) {
      v = Opdef::add(v, o.v);
      return *this;
    }else static_assert("either subst_add or add is needed.");

  }
  MyAlg operator +(const MyAlg& o) const { 
    if constexpr (has_add<Opdef>::value) {
      return MyAlg(Opdef::add(v, o.v));
    }else if constexpr (has_subst_add<Opdef>::value) {
      MyAlg ret(v);
      Opdef::subst_add(ret.v, o.v);
      return ret;
    }else static_assert("either subst_add or add is needed.");
  }
  MyAlg& operator *=(const MyAlg& o) { 
    if constexpr (has_subst_mult<Opdef>::value) {
      Opdef::subst_mult(v, o.v);
      return *this;
    }else if constexpr (has_mult<Opdef>::value) {
      v = Opdef::mult(v, o.v);
      return *this;
    }else static_assert("either subst_mult or mult is needed.");

  }
  MyAlg operator *(const MyAlg& o) const { 
    if constexpr (has_mult<Opdef>::value) {
      return MyAlg(Opdef::mult(v, o.v));
    }else if constexpr (has_subst_mult<Opdef>::value) {
      MyAlg ret(v);
      Opdef::subst_mult(ret.v, o.v);
      return ret;
    }else static_assert("either subst_mult or mult is needed.");
  }
  MyAlg& operator -=(const MyAlg& o) { 
    if constexpr (has_subst_subt<Opdef>::value) {
      Opdef::subst_subt(v, o.v);
      return *this;
    }else if constexpr (has_subt<Opdef>::value) {
      v = Opdef::subt(v, o.v);
      return *this;
    }else static_assert("either subst_subt or subt is needed.");

  }
  MyAlg operator -(const MyAlg& o) const { 
    if constexpr (has_subt<Opdef>::value) {
      return MyAlg(Opdef::subt(v, o.v));
    }else if constexpr (has_subst_subt<Opdef>::value) {
      MyAlg ret(v);
      Opdef::subst_subt(ret.v, o.v);
      return ret;
    }else static_assert("either subst_subt or subt is needed.");
  }
  friend istream& operator >>(istream& is, MyAlg& t)       { is >> t.v; return is; }
  friend ostream& operator <<(ostream& os, const MyAlg& t) { os << t.v; return os; }
};





// ---- end algOp.cc

// ---- inserted function f:gcd from util.cc

tuple<ll, ll, ll> mut_div(ll a, ll b, ll c, bool eff_c = true) {
  // auto [g, s, t] = mut_div(a, b, c, eff_c)
  //    If eff_c is true (default),
  //        g == gcd(|a|, |b|) and as + bt == c, if such s,t exists
  //        (g, s, t) == (-1, -1, -1)            otherwise
  //    If eff_c is false,                                 
  //        g == gcd(|a|, |b|) and as + bt == g           
  //    N.b.  gcd(0, t) == gcd(t, 0) == t.
  if (a == 0) {
    if (eff_c) {
      if (c % b != 0) return {-1, -1, -1};
      else            return {abs(b), 0, c / b};
    }else {
      if (b < 0) return {-b, 0, -1};
      else       return { b, 0,  1};
    }
  }else {
    auto [g, t, u] = mut_div(b % a, a, c, eff_c);
    // DLOGK(b%a, a, c, g, t, u);
    if (g == -1) return {-1, -1, -1};
    return {g, u - (b / a) * t, t};
  }
}

// auto [g, s, t] = eGCD(a, b)  --->  sa + tb == g == gcd(|a|, |b|)
//    N.b.  gcd(0, t) == gcd(t, 0) == t.
tuple<ll, ll, ll> eGCD(ll a, ll b) { return mut_div(a, b, 0, false); }

pair<ll, ll> crt_sub(ll a1, ll x1, ll a2, ll x2) {
  // DLOGKL("crt_sub", a1, x1, a2, x2);
  a1 = a1 % x1;
  a2 = a2 % x2;
  auto [g, s, t] = mut_div(x1, -x2, a2 - a1);
  // DLOGK(g, s, t);
  if (g == -1) return {-1, -1};
  ll z = x1 / g * x2;
  // DLOGK(z);
  s = s % (x2 / g);
  ll r = (x1 * s + a1) % z;
  // DLOGK(r);
  if (r < 0) r += z;
  // DLOGK(r);
  return {r, z};
};

// Chinese Remainder Theorem
//
//    r = crt(a1, x1, a2, x2)
//    ==>   r = a1 (mod x1);  r = a2 (mod x2);  0 <= r < lcm(x1, x2)
//    If no such r exists, returns -1
//    Note: x1 and x2 should >= 1.  a1 and a2 can be negative or zero.
//
//    r = crt(as, xs)
//    ==>   for all i. r = as[i] (mod xs[i]); 0 <= r < lcm(xs)
//    If no such r exists, returns -1
//    Note: xs[i] should >= 1.  as[i] can be negative or zero.
//          It should hold: len(xs) == len(as) > 0

ll crt(ll a1, ll x1, ll a2, ll x2) { return crt_sub(a1, x1, a2, x2).first; }

ll crt(vector<ll> as, vector<ll> xs) {
  // DLOGKL("crt", as, xs);
  assert(xs.size() == as.size() && xs.size() > 0);
  ll r = as[0];
  ll z = xs[0];
  for (size_t i = 1; i < xs.size(); i++) {
    // DLOGK(i, r, z, as[i], xs[i]);
    tie(r, z) = crt_sub(r, z, as[i], xs[i]);
    // DLOGK(r, z);
    if (r == -1) return -1;
  }
  return r;
}

// ---- end f:gcd

// ---- inserted library file mod.cc

template<int mod=0>
struct FpG {   // G for General
  static ll dyn_mod;

  static ll getMod() {
    if (mod == 0) return dyn_mod;
    else          return mod;
  }

  static void setMod(ll _mod) {  // effective only when mod == 0
    dyn_mod = _mod;
  }

  static ll _conv(ll x) {
    if (x >= getMod())  return x % getMod();
    if (x >= 0)         return x;
    if (x >= -getMod()) return x + getMod();
    ll y = x % getMod();
    if (y == 0) return 0;
    return y + getMod();
  }

  ll val;

  FpG(int t = 0) : val(_conv(t)) {}
  FpG(ll t) : val(_conv(t)) {}
  FpG(const FpG& t) : val(t.val) {}
  FpG& operator =(const FpG& t) { val = t.val; return *this; }
  FpG& operator =(ll t) { val = _conv(t); return *this; }
  FpG& operator =(int t) { val = _conv(t); return *this; }

  FpG& operator +=(const FpG& t) {
    val += t.val;
    if (val >= getMod()) val -= getMod();
    return *this;
  }

  FpG& operator -=(const FpG& t) {
    val -= t.val;
    if (val < 0) val += getMod();
    return *this;
  }

  FpG& operator *=(const FpG& t) {
    val = (val * t.val) % getMod();
    return *this;
  }

  FpG inv() const {
    if (val == 0) {
      throw runtime_error("FpG::inv(): called for zero.");
    }
    auto [g, u, v] = eGCD(val, getMod());
    return FpG(u);
  }

  FpG zero() const { return (FpG)0; }
  FpG one() const { return (FpG)1; }
  FpG inverse() const { return inv(); }

  FpG& operator /=(const FpG& t) {
    return (*this) *= t.inv();
  }

  FpG operator +(const FpG& t) const { return FpG(val) += t; }
  FpG operator -(const FpG& t) const { return FpG(val) -= t; }
  FpG operator *(const FpG& t) const { return FpG(val) *= t; }
  FpG operator /(const FpG& t) const { return FpG(val) /= t; }
  FpG operator -() const { return FpG(-val); }

  bool operator ==(const FpG& t) const { return val == t.val; }
  bool operator !=(const FpG& t) const { return val != t.val; }
  
  operator ll() const { return val; }

  friend FpG operator +(int x, const FpG& y) { return FpG(x) + y; }
  friend FpG operator -(int x, const FpG& y) { return FpG(x) - y; }
  friend FpG operator *(int x, const FpG& y) { return FpG(x) * y; }
  friend FpG operator /(int x, const FpG& y) { return FpG(x) / y; }
  friend bool operator ==(int x, const FpG& y) { return FpG(x) == y; }
  friend bool operator !=(int x, const FpG& y) { return FpG(x) != y; }
  friend FpG operator +(ll x, const FpG& y) { return FpG(x) + y; }
  friend FpG operator -(ll x, const FpG& y) { return FpG(x) - y; }
  friend FpG operator *(ll x, const FpG& y) { return FpG(x) * y; }
  friend FpG operator /(ll x, const FpG& y) { return FpG(x) / y; }
  friend bool operator ==(ll x, const FpG& y) { return FpG(x) == y; }
  friend bool operator !=(ll x, const FpG& y) { return FpG(x) != y; }
  friend FpG operator +(const FpG& x, int y) { return x + FpG(y); }
  friend FpG operator -(const FpG& x, int y) { return x - FpG(y); }
  friend FpG operator *(const FpG& x, int y) { return x * FpG(y); }
  friend FpG operator /(const FpG& x, int y) { return x / FpG(y); }
  friend bool operator ==(const FpG& x, int y) { return x == FpG(y); }
  friend bool operator !=(const FpG& x, int y) { return x != FpG(y); }
  friend FpG operator +(const FpG& x, ll y) { return x + FpG(y); }
  friend FpG operator -(const FpG& x, ll y) { return x - FpG(y); }
  friend FpG operator *(const FpG& x, ll y) { return x * FpG(y); }
  friend FpG operator /(const FpG& x, ll y) { return x / FpG(y); }
  friend bool operator ==(const FpG& x, ll y) { return x == FpG(y); }
  friend bool operator !=(const FpG& x, ll y) { return x != FpG(y); }

  friend istream& operator>> (istream& is, FpG& t) {
    ll x; is >> x;
    t = x;
    return is;
  }

  friend ostream& operator<< (ostream& os, const FpG& t) {
    os << t.val;
    return os;
  }

};
template<int mod>
ll FpG<mod>::dyn_mod;

template<int mod=0>
class CombG {
  int nMax;
  vector<FpG<mod>> vFact;
  vector<FpG<mod>> vInvFact;
public:
  CombG(int nm) : nMax(nm), vFact(nm+1), vInvFact(nm+1) {
    vFact.at(0) = 1;
    for (int i = 1; i <= nMax; i++) vFact.at(i) = i * vFact.at(i-1);
    vInvFact.at(nMax) = vFact.at(nMax).inv();
    for (int i = nMax; i >= 1; i--) vInvFact.at(i-1) = i * vInvFact.at(i);
  }
  FpG<mod> fact(int n) { return vFact.at(n); }
  FpG<mod> comb(int n, int r) {
    if (r < 0 || r > n) return 0;
    return vFact.at(n) * vInvFact.at(r) * vInvFact.at(n-r);
  }
  // The number of permutation extracting r from n.
  FpG<mod> perm(int n, int r) {
    return vFact.at(n) * vInvFact.at(n-r);
  }
};

constexpr int primeA = 1'000'000'007;
constexpr int primeB = 998'244'353;          // '
using FpA = FpG<primeA>;
using FpB = FpG<primeB>;
using CombA = CombG<primeA>;
using CombB = CombG<primeB>;

// ---- end mod.cc

// ---- inserted function f:<< from util.cc
template <typename T1, typename T2>
ostream& operator<< (ostream& os, const pair<T1,T2>& p) {
  os << "(" << p.first << ", " << p.second << ")";
  return os;
}

template <typename T1, typename T2, typename T3>
ostream& operator<< (ostream& os, const tuple<T1,T2,T3>& t) {
  os << "(" << get<0>(t) << ", " << get<1>(t)
     << ", " << get<2>(t) << ")";
  return os;
}

template <typename T1, typename T2, typename T3, typename T4>
ostream& operator<< (ostream& os, const tuple<T1,T2,T3,T4>& t) {
  os << "(" << get<0>(t) << ", " << get<1>(t)
     << ", " << get<2>(t) << ", " << get<3>(t) << ")";
  return os;
}

template <typename T>
ostream& operator<< (ostream& os, const vector<T>& v) {
  os << '[';
  for (auto it = v.begin(); it != v.end(); it++) {
    if (it != v.begin()) os << ", ";
    os << *it;
  }
  os << ']';

  return os;
}

template <typename T, typename C>
ostream& operator<< (ostream& os, const set<T, C>& v) {
  os << '{';
  for (auto it = v.begin(); it != v.end(); it++) {
    if (it != v.begin()) os << ", ";
    os << *it;
  }
  os << '}';

  return os;
}

template <typename T, typename C>
ostream& operator<< (ostream& os, const unordered_set<T, C>& v) {
  os << '{';
  for (auto it = v.begin(); it != v.end(); it++) {
    if (it != v.begin()) os << ", ";
    os << *it;
  }
  os << '}';

  return os;
}

template <typename T, typename C>
ostream& operator<< (ostream& os, const multiset<T, C>& v) {
  os << '{';
  for (auto it = v.begin(); it != v.end(); it++) {
    if (it != v.begin()) os << ", ";
    os << *it;
  }
  os << '}';

  return os;
}

template <typename T1, typename T2, typename C>
ostream& operator<< (ostream& os, const map<T1, T2, C>& mp) {
  os << '[';
  for (auto it = mp.begin(); it != mp.end(); it++) {
    if (it != mp.begin()) os << ", ";
    os << it->first << ": " << it->second;
  }
  os << ']';

  return os;
}

template <typename T1, typename T2, typename C>
ostream& operator<< (ostream& os, const unordered_map<T1, T2, C>& mp) {
  os << '[';
  for (auto it = mp.begin(); it != mp.end(); it++) {
    if (it != mp.begin()) os << ", ";
    os << it->first << ": " << it->second;
  }
  os << ']';

  return os;
}

template <typename T, typename T2>
ostream& operator<< (ostream& os, const queue<T, T2>& orig) {
  queue<T, T2> que(orig);
  bool first = true;
  os << '[';
  while (!que.empty()) {
    T x = que.front(); que.pop();
    if (!first) os << ", ";
    os << x;
    first = false;
  }
  return os << ']';
}

template <typename T, typename T2>
ostream& operator<< (ostream& os, const deque<T, T2>& orig) {
  deque<T, T2> que(orig);
  bool first = true;
  os << '[';
  while (!que.empty()) {
    T x = que.front(); que.pop_front();
    if (!first) os << ", ";
    os << x;
    first = false;
  }
  return os << ']';
}

template <typename T, typename T2, typename T3>
ostream& operator<< (ostream& os, const priority_queue<T, T2, T3>& orig) {
  priority_queue<T, T2, T3> pq(orig);
  bool first = true;
  os << '[';
  while (!pq.empty()) {
    T x = pq.top(); pq.pop();
    if (!first) os << ", ";
    os << x;
    first = false;
  }
  return os << ']';
}

template <typename T>
ostream& operator<< (ostream& os, const stack<T>& st) {
  stack<T> tmp(st);
  os << '[';
  bool first = true;
  while (!tmp.empty()) {
    T& t = tmp.top();
    if (first) first = false;
    else os << ", ";
    os << t;
    tmp.pop();
  }
  os << ']';
  return os;
}

#if __cplusplus >= 201703L
template <typename T>
ostream& operator<< (ostream& os, const optional<T>& t) {
  if (t.has_value()) os << "v(" << t.value() << ")";
  else               os << "nullopt";
  return os;
}
#endif

ostream& operator<< (ostream& os, int8_t x) {
  os << (int32_t)x;
  return os;
}

// ---- end f:<<

// ---- inserted library file debug.cc
template <class... Args>
string dbgFormat(const char* fmt, Args... args) {
  size_t len = snprintf(nullptr, 0, fmt, args...);
  char buf[len + 1];
  snprintf(buf, len + 1, fmt, args...);
  return string(buf);
}

template <class Head>
void dbgLog(bool with_nl, Head&& head) {
  cerr << head;
  if (with_nl) cerr << endl;
}

template <class Head, class... Tail>
void dbgLog(bool with_nl, Head&& head, Tail&&... tail)
{
  cerr << head << " ";
  dbgLog(with_nl, forward<Tail>(tail)...);
}

#if DEBUG
  #define DLOG(...)        dbgLog(true, __VA_ARGS__)
  #define DLOGNNL(...)     dbgLog(false, __VA_ARGS__)
  #define DFMT(...)        cerr << dbgFormat(__VA_ARGS__) << endl
  #define DCALL(func, ...) func(__VA_ARGS__)
#else
  #define DLOG(...)
  #define DLOGNNL(...)
  #define DFMT(...)
  #define DCALL(func, ...)
#endif

/*
#if DEBUG_LIB
  #define DLOG_LIB(...)        dbgLog(true, __VA_ARGS__)
  #define DLOGNNL_LIB(...)     dbgLog(false, __VA_ARGS__)
  #define DFMT_LIB(...)        cerr << dbgFormat(__VA_ARGS__) << endl
  #define DCALL_LIB(func, ...) func(__VA_ARGS__)
#else
  #define DLOG_LIB(...)
  #define DFMT_LIB(...)
  #define DCALL_LIB(func, ...)
#endif
*/

#define DUP1(E1)       #E1 "=", E1
#define DUP2(E1,E2)    DUP1(E1), DUP1(E2)
#define DUP3(E1,...)   DUP1(E1), DUP2(__VA_ARGS__)
#define DUP4(E1,...)   DUP1(E1), DUP3(__VA_ARGS__)
#define DUP5(E1,...)   DUP1(E1), DUP4(__VA_ARGS__)
#define DUP6(E1,...)   DUP1(E1), DUP5(__VA_ARGS__)
#define DUP7(E1,...)   DUP1(E1), DUP6(__VA_ARGS__)
#define DUP8(E1,...)   DUP1(E1), DUP7(__VA_ARGS__)
#define DUP9(E1,...)   DUP1(E1), DUP8(__VA_ARGS__)
#define DUP10(E1,...)   DUP1(E1), DUP9(__VA_ARGS__)
#define DUP11(E1,...)   DUP1(E1), DUP10(__VA_ARGS__)
#define DUP12(E1,...)   DUP1(E1), DUP11(__VA_ARGS__)
#define GET_MACRO(_1,_2,_3,_4,_5,_6,_7,_8,_9,_10,_11,_12,NAME,...) NAME
#define DUP(...)          GET_MACRO(__VA_ARGS__, DUP12, DUP11, DUP10, DUP9, DUP8, DUP7, DUP6, DUP5, DUP4, DUP3, DUP2, DUP1)(__VA_ARGS__)
#define DLOGK(...)        DLOG(DUP(__VA_ARGS__))
#define DLOGKL(lab, ...)  DLOG(lab, DUP(__VA_ARGS__))

#if DEBUG_LIB
  #define DLOG_LIB   DLOG
  #define DLOGK_LIB  DLOGK
  #define DLOGKL_LIB DLOGKL
#endif

// ---- end debug.cc

// @@ !! LIM -- end mark --

using Fp = FpB;
using Comb = CombB;

int main(/* int argc, char *argv[] */) {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout << setprecision(20);

  ll N, K; cin >> N >> K;
  vector<ll> A(N); REP(i, N) cin >> A[i];
  
  vector<Fp> as = {1};
  REP(i, N) {
    vector<Fp> prev = as;
    ll sz = SIZE(prev);
    as.resize(sz + 1);
    copy_backward(as.begin(), as.begin() + sz, as.begin() + sz + 1);
    as[0] = 0;
    REP(j, sz) as[j] += prev[j] * A[i];
  }
  DLOGK(as);
  Fp perm = 1, pow = 1, ans = 0;
  REP(i, N + 1) {
    ans += as[i] * perm / pow;
    perm *= (K - i);
    pow *= N;
  }
  cout << ans << endl;

  return 0;
}

提出情報

ジャッジ結果