結果

問題 No.612 Move on grid
ユーザー niuez
提出日時 2021-11-05 15:37:45
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
WA  
実行時間 -
コード長 12,257 bytes
コンパイル時間 3,618 ms
コンパイル使用メモリ 222,148 KB
最終ジャッジ日時 2025-01-25 11:53:24
ジャッジサーバーID
（参考情報） 		judge4 / judge1
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 2 WA * 2
other AC * 2 WA * 15
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 #
プレゼンテーションモードにする

#include <bits/stdc++.h>
using namespace std;
using i64 = long long;
#define rep(i,s,e) for(i64 (i) = (s);(i) < (e);(i)++)
#define all(x) x.begin(),x.end()
#define STRINGIFY(n) #n
#define TOSTRING(n) STRINGIFY(n)
#define PREFIX "#" TOSTRING(__LINE__) "| "
#define debug(x) \
{ \
  std::cout << PREFIX << #x << " = " << x << std::endl; \
}
std::ostream& output_indent(std::ostream& os, int ind) {
  for(int i = 0; i < ind; i++) os << " ";
  return os;
}
template<class S, class T> std::ostream& operator<<(std::ostream& os, const std::pair<S, T>& p);
template<class T> std::ostream& operator<<(std::ostream& os, const std::vector<T>& v);
template<class S, class T> std::ostream& operator<<(std::ostream& os, const std::pair<S, T>& p) {
  return (os << "(" << p.first << ", " << p.second << ")");
}
template<class T> std::ostream& operator<<(std::ostream& os, const std::vector<T>& v) {
  os << "[";
  for(int i = 0;i < v.size();i++) os << v[i] << ", ";
  return (os << "]");
}
template<class T>
static inline std::vector<T> ndvec(size_t&& n, T val) { return std::vector<T>(n, std::forward<T>(val)); }
template<class... Tail>
static inline auto ndvec(size_t&& n, Tail&&... tail) {
  return std::vector<decltype(ndvec(std::forward<Tail>(tail)...))>(n, ndvec(std::forward<Tail>(tail)...));
}
template<class Cond> struct chain {
  Cond cond; chain(Cond cond) : cond(cond) {}
  template<class T> bool operator()(T& a, const T& b) const { if(cond(a, b)) { a = b; return true; } return false; }
};
template<class Cond> chain<Cond> make_chain(Cond cond) { return chain<Cond>(cond); }
#include <iostream>
using i64 = long long;
template<i64 M> struct modint { i64 a;
  constexpr modint(const i64 x = 0): a((x%M+M)%M){}
  constexpr i64 value() const { return a; }
  constexpr modint inv() const { return this->pow(M-2); }
  constexpr modint pow(i64 r) const {
    modint ans(1); modint aa = *this;
    while(r) { if(r & 1) ans *= aa; aa *= aa; r >>= 1; }
    return ans;
  }
  constexpr modint& operator=(const i64 r) { a = (r % M + M) % M; return *this; }
  constexpr modint& operator+=(const modint r) { a += r.a; if(a >= M) a -= M; return *this; }
  constexpr modint& operator-=(const modint r) { a -= r.a; if(a < 0) a += M; return *this; }
  constexpr modint& operator*=(const modint r) { a = a * r.a % M; return *this; }
  constexpr modint& operator/=(const modint r) { (*this) *= r.inv(); return *this; }
  constexpr modint operator+(const modint r) const { return modint(*this) += r; }
  constexpr modint operator-(const modint r) const { return modint(*this) -= r; }
  constexpr modint operator*(const modint r) const { return modint(*this) *= r; }
  constexpr modint operator/(const modint r) const { return modint(*this) /= r; }
  constexpr bool operator!=(const modint r) const { return this->value() != r.value(); }
};
template<const i64 M> std::ostream& operator<<(std::ostream& os, const modint<M>& m) { os << m.value(); return os; }
#include <vector>
using namespace std;
constexpr i64 NTT_PRIMES[][2] = {
    {1224736769, 3}, // 2^24 * 73 + 1,
    {1053818881, 7}, // 2^20 * 3 * 5 * 67 + 1
    {1051721729, 6}, // 2^20 * 17 * 59 + 1
    {1045430273, 3}, // 2^20 * 997 + 1
    {1012924417, 5}, // 2^21 * 3 * 7 * 23 + 1
    {1007681537, 3}, // 2^20 * 31^2 + 1
    {1004535809, 3}, // 2^21 * 479 + 1
    {998244353, 3},  // 2^23 * 7 * 17 + 1
    {985661441, 3},  // 2^22 * 5 * 47 + 1
    {976224257, 3},  // 2^20 * 7^2 * 19 + 1
    {975175681, 17}, // 2^21 * 3 * 5 * 31 + 1
    {962592769, 7},  // 2^21 * 3^3 * 17 + 1
    {950009857, 7},  // 2^21 * 4 * 151 + 1
    {943718401, 7},  // 2^22 * 3^2 * 5^2 + 1
    {935329793, 3},  // 2^22 * 223 + 1
    {924844033, 5},  // 2^21 * 3^2 * 7^2 + 1
    {469762049, 3},  // 2^26 * 7 + 1
    {167772161, 3},  // 2^25 * 5 + 1
};
template<const i64 mod, const i64 primitive>
vector<modint<mod>> number_theoretic_transform(vector<modint<mod>> a) {
  i64 n = a.size();
  for(i64 s = n >> 1; s >= 1; s >>= 1) {
    modint<mod> zeta = modint<mod>(primitive).pow((mod - 1) / (s << 1));
    for(i64 i = 0; i < n; i += (s << 1)) {
      modint<mod> zi = 1;
      for(i64 j = 0;j < s;j++) {
        modint<mod> t = a[i + j] - a[s + i + j];
        a[i + j] += a[s + i + j];
        a[s + i + j] = t * zi;
        zi = zi * zeta;
      }
    }
  }
  return a;
}
template<const i64 mod, const i64 primitive>
vector<modint<mod>> inverse_number_theoretic_transform(vector<modint<mod>> a) {
  i64 n = a.size();
  for(i64 s = 1; s < n; s <<= 1) {
    modint<mod> zeta = modint<mod>(primitive).pow((mod - 1) / (s << 1)).pow(mod - 2);
    for(i64 i = 0; i < n; i += (s << 1)) {
      modint<mod> zi = 1;
      for(i64 j = 0;j < s;j++) {
        modint<mod> t = a[s + i + j] * zi;
        a[s + i + j] = a[i + j] - t;
        a[i + j] = a[i + j] + t;
        zi = zi * zeta;
      }
    }
  }
  auto inv_n = modint<mod>(n).pow(mod - 2);
  for(int i = 0;i < n;i++) a[i] *= inv_n;
  return a;
}
template<const i64 mod, const i64 primitive>
struct fps_ntt_multiply {
  using fps_type = modint<mod>;
  using conv_type = modint<mod>;
  static std::vector<conv_type> dft(std::vector<fps_type> arr) {
    return number_theoretic_transform<mod, primitive>(std::move(arr));
  }
  static std::vector<fps_type> idft(std::vector<conv_type> arr) {
    return inverse_number_theoretic_transform<mod, primitive>(std::move(arr));
  }
  static std::vector<conv_type> multiply(std::vector<conv_type> a, std::vector<conv_type> b) {
    for(int i = 0;i < a.size();i++) a[i] *= b[i];
    return a;
  }
};
#include <tuple>
#include <bits/stdc++.h>
using namespace std;
using i64 = long long;
i64 pow_mod(i64 x, i64 r, i64 mod) {
  i64 ans = 1;
  while(r) {
    if(r & 1) ans = (ans * x) % mod;
    r >>= 1;
    x = x * x % mod;
  }
  return ans;
}
i64 inv_mod(i64 x, i64 mod) {
  return pow_mod(x, mod - 2, mod);
}
i64 garner(const vector<i64> &x, vector<i64> mods, i64 mod) {
  mods.emplace_back(mod);
  vector<i64> coeffs(x.size() + 1, 1);
  vector<i64> constants(x.size() + 1, 0);
  for(i64 i = 0; i < x.size(); i++) {
    i64 v = (x[i] - constants[i]) * inv_mod(coeffs[i], mods[i]) % mods[i];
    if(v < 0) v += mods[i];
    for(i64 j = i + 1; j < x.size() + 1; j++) {
      constants[j] = (constants[j] + coeffs[j] * v) % mods[j];
      coeffs[j] = (coeffs[j] * mods[i]) % mods[j];
    }
  }
  return constants.back();
}
template<i64 M, i64... NTTis>
struct fps_multiply_arb {
  using fps_type = std::vector<modint<M>>;
  using conv_type = std::tuple<std::vector<modint<NTT_PRIMES[NTTis][0]>>...>;
  const static std::size_t tsize = std::tuple_size<conv_type>::value;
  template<i64 M2, i64 primitive>
  static std::vector<modint<M2>> dft_m2(const fps_type& arr) {
    std::vector<modint<M2>> res(arr.size());
    for(std::size_t i = 0; i < arr.size(); i++)
      res[i] = modint<M2>(arr[i].value());
    return number_theoretic_transform<M2, primitive>(std::move(res));
  }
  template<i64 M2, i64 primitive>
  static std::vector<modint<M2>> idft_m2(std::vector<modint<M2>> arr) {
    return inverse_number_theoretic_transform<M2, primitive>(std::move(arr));
  }
  template<std::size_t... I>
  static fps_type idft_func(std::index_sequence<I...>, conv_type arr) {
    arr = std::make_tuple(idft_m2<NTT_PRIMES[NTTis][0], NTT_PRIMES[NTTis][1]>(std::get<I>(arr))...);
    std::size_t len = std::get<0>(arr).size();
    static std::vector<i64> primes = { NTT_PRIMES[NTTis][0]... };
    fps_type res(len);
    for(std::size_t i = 0; i < len; i++) {
      std::vector<i64> x = { std::get<I>(arr)[i].value()... };
      res[i] = modint<M>(garner(x, primes, M));
    }
    return std::move(res);
  }
  template<i64 M2>
  static char mult_m2(std::vector<modint<M2>>& a, const std::vector<modint<M2>>& b) {
    for(int i = 0;i < a.size();i++) a[i] *= b[i];
    return 0;
  }
  template<std::size_t... I>
  static void mult_func(std::index_sequence<I...>, conv_type& a, const conv_type& b) {
    auto res = std::make_tuple(mult_m2<NTT_PRIMES[NTTis][0]>(std::get<I>(a), std::get<I>(b))...);
  }
  static conv_type dft(fps_type arr) {
    return std::make_tuple(dft_m2<NTT_PRIMES[NTTis][0], NTT_PRIMES[NTTis][1]>(arr)...);
  }
  static fps_type idft(conv_type arr) {
    return idft_func(std::make_index_sequence<tsize>(), std::move(arr));
  }
  static conv_type multiply(conv_type a, const conv_type& b) {
    mult_func(std::make_index_sequence<tsize>(), a, b);
    return a;
  }
};
/*template<typename _Size>
  inline _Size
  __lg(_Size __n)
  {
    _Size __k;
    for (__k = 0; __n != 0; __n >>= 1)
  ++__k;
    return __k - 1;
  }*/
template<class T, class fps_multiply>
struct FPS {
  std::vector<T> coef;
  static std::size_t bound_pow2(std::size_t sz) {
    return 1ll << (__lg(sz - 1) + 1);
  }
  
  FPS(const std::vector<T>& arr): coef(arr) {}
  size_t size() const { return coef.size(); }
  void bound_resize() {
    this->coef.resize(bound_pow2(this->size()));
  }
  T operator[](int i) const {
    if(i < coef.size()) return coef[i];
    else return T();
  }
  T & operator[](int i) { return coef[i]; }
  FPS pre(int n) const {
    std::vector<T> nex(n);
    for(int i = 0;i < coef.size() && i < n; i++) nex[i] = coef[i];
    return FPS(nex);
  }
  
  // F(0) must not be 0
  FPS inv() {
    FPS g = FPS(std::vector<T>{ T(1) / (*this)[0] });
    this->bound_resize();
    i64 n = this->size();
    for(int i = 1;i < n;i <<= 1) {
      g = g.pre(i << 1);
      auto gdft = fps_multiply::dft(g.coef);
      auto e = fps_multiply::idft(
          fps_multiply::multiply(
            fps_multiply::dft(this->pre(i << 1).coef), gdft
            )
          );
      for(int j = 0;j < i;j++) {
        e[j] = T(0);
        e[j + i] = e[j + i] * T(-1);
      }
      auto f = fps_multiply::idft(
          fps_multiply::multiply(
            fps_multiply::dft(e), std::move(gdft)
            )
          );
      for(int j = 0;j < i;j++) {
        f[j] = g[j];
      }
      g.coef = std::move(f);
    }
    return g.pre(n);
  }
  FPS diff() const {
    FPS res(vector<T>(this->size() - 1, T(0)));
    for(i64 i = 1;i < this->size();i++) res[i - 1] = coef[i] * T(i);
    return res;
  }
  FPS integral() const {
    FPS res(vector<T>(this->size() + 1, T(0)));
    for(i64 i = 0;i < this->size();i++) res[i + 1] = coef[i] / T(i + 1);
    return res;
  }
  // F(0) must be 0
  FPS log() {
    return (this->diff() * this->inv()).integral().pre(this->size());
  }
  FPS exp() const {
    FPS f(vector<T>{ T(1) });
    FPS g = *this;
    g.bound_resize();
    g[0] += T(1);
    for(i64 i = 1;i < size();i <<= 1 ) {
      f = (f * (g.pre(i << 1) - f.pre(i << 1).log())).pre(i << 1);
    }
    return f;
  }
  
  FPS operator+(const FPS& rhs) {
    i64 n = std::max(this->size(), rhs.size());
    std::vector<T> ans(n);
    for(int i = 0;i < n;i++) ans[i] = (*this)[i] + rhs[i];
    return FPS(ans);
  }
  FPS operator-(const FPS& rhs) {
    i64 n = std::max(this->size(), rhs.size());
    std::vector<T> ans(n);
    for(int i = 0;i < n;i++) ans[i] = (*this)[i] - rhs[i];
    return FPS(ans);
  }
  FPS operator*(const FPS& rhs) {
    i64 m = this->size() + rhs.size() - 1;
    i64 n = bound_pow2(m);
    auto res = fps_multiply::idft(
        fps_multiply::multiply(
          fps_multiply::dft(this->pre(n).coef), fps_multiply::dft(rhs.pre(n).coef)
          )
        );
    res.resize(m);
    return res;
  }
  FPS& operator*=(const T& x) {
    for(int i = 0;i < this->size();i++) {
      (*this)[i] *= x;
    }
    return *this;
  }
};
int main() {
  i64 T;
  cin >> T;
  i64 a, b, c, d, e;
  cin >> a >> b >> c >> d >> e;
  i64 shift = std::max({std::abs(a), std::abs(b), std::abs(c)});
  using fp = modint<1000000007>;
  using fps = FPS<fp, fps_multiply_arb<1000000007, 0, 1, 2>>;
  //using fp = modint<998244353>;
  //using fps = FPS<fp, fps_ntt_multiply<998244353, 3>>;
  vector<fp> init(shift * 2 + 1);
  init[a + shift] += 1;
  init[b + shift] += 1;
  init[c + shift] += 1;
  init[-a + shift] += 1;
  init[-b + shift] += 1;
  init[-c + shift] += 1;
  fps f(init);
  fps ans(std::vector<fp>{ fp(1) });
  i64 t = T;
  while(t) {
    if(t & 1) {
      ans = ans * f;
    }
    t >>= 1;
    f = f * f;
  }
  fp res = 0;
  rep(i,d,e + 1) {
    if(i < ans.size()) {
      res += ans[i + shift * T];
    }
  }
  cout << res.a << endl;
}
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