#898776 (C++17) No.2406 Difference of Coordinate Squared

提出ソース
結果

問題	No.2406 Difference of Coordinate Squared
コンテスト
ユーザー	tonegawa
提出日時	2023-08-04 23:00:27
言語	C++17 (gcc 13.3.0 + boost 1.87.0)
結果	WA
実行時間	-
コード長	20,056 bytes
コンパイル時間	1,380 ms
コンパイル使用メモリ	139,224 KB
最終ジャッジ日時	2025-02-15 23:14:04
ジャッジサーバーID （参考情報）	judge3 / judge2
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
other	AC * 47 WA * 8
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ソースコード

raw source code
#line 1 ".lib/template.hpp"


#include <iostream>
#include <string>
#include <vector>
#include <array>
#include <tuple>
#include <stack>
#include <queue>
#include <deque>
#include <algorithm>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <bitset>
#include <cmath>
#include <functional>
#include <cassert>
#include <climits>
#include <iomanip>
#include <numeric>
#include <memory>
#include <random>
#include <thread>
#include <chrono>
#define allof(obj) (obj).begin(), (obj).end()
#define range(i, l, r) for(int i=l;i<r;i++)
#define bit_subset(i, S) for(int i=S, zero_cnt=0;(zero_cnt+=i==S)<2;i=(i-1)&S)
#define bit_kpop(i, n, k) for(int i=(1<<k)-1,x_bit,y_bit;i<(1<<n);x_bit=(i&-i),y_bit=i+x_bit,i=(!i?(1<<n):((i&~y_bit)/x_bit>>1)|y_bit))
#define bit_kth(i, k) ((i >> k)&1)
#define bit_highest(i) (i?63-__builtin_clzll(i):-1)
#define bit_lowest(i) (i?__builtin_ctzll(i):-1)
#define sleepms(t) std::this_thread::sleep_for(std::chrono::milliseconds(t))
using ll = long long;
using ld = long double;
using ul = uint64_t;
using pi = std::pair<int, int>;
using pl = std::pair<ll, ll>;
using namespace std;

template<typename F, typename S>
std::ostream &operator<<(std::ostream &dest, const std::pair<F, S> &p){
  dest << p.first << ' ' << p.second;
  return dest;
}
template<typename T>
std::ostream &operator<<(std::ostream &dest, const std::vector<std::vector<T>> &v){
  int sz = v.size();
  if(sz==0) return dest;
  for(int i=0;i<sz;i++){
    int m = v[i].size();
    for(int j=0;j<m;j++) dest << v[i][j] << (i!=sz-1&&j==m-1?'\n':' ');
  }
  return dest;
}
template<typename T>
std::ostream &operator<<(std::ostream &dest, const std::vector<T> &v){
  int sz = v.size();
  if(sz==0) return dest;
  for(int i=0;i<sz-1;i++) dest << v[i] << ' ';
  dest << v[sz-1];
  return dest;
}
template<typename T, size_t sz>
std::ostream &operator<<(std::ostream &dest, const std::array<T, sz> &v){
  if(sz==0) return dest;
  for(int i=0;i<sz-1;i++) dest << v[i] << ' ';
  dest << v[sz-1];
  return dest;
}
template<typename T>
std::ostream &operator<<(std::ostream &dest, const std::set<T> &v){
  for(auto itr=v.begin();itr!=v.end();){
    dest << *itr;
    itr++;
    if(itr!=v.end()) dest << ' ';
  }
  return dest;
}
template<typename T, typename E>
std::ostream &operator<<(std::ostream &dest, const std::map<T, E> &v){
  for(auto itr=v.begin();itr!=v.end();){
    dest << '(' << itr->first << ", " << itr->second << ')';
    itr++;
    if(itr!=v.end()) dest << '\n';
  }
  return dest;
}
template<typename T>
vector<T> make_vec(size_t sz, T val){return std::vector<T>(sz, val);}
template<typename T, typename... Tail>
auto make_vec(size_t sz, Tail ...tail){
  return std::vector<decltype(make_vec<T>(tail...))>(sz, make_vec<T>(tail...));
}
template<typename T>
vector<T> read_vec(size_t sz){
  std::vector<T> v(sz);
  for(int i=0;i<(int)sz;i++) std::cin >> v[i];
  return v;
}
template<typename T, typename... Tail>
auto read_vec(size_t sz, Tail ...tail){
  auto v = std::vector<decltype(read_vec<T>(tail...))>(sz);
  for(int i=0;i<(int)sz;i++) v[i] = read_vec<T>(tail...);
  return v;
}
void io_init(){
  std::cin.tie(nullptr);
  std::ios::sync_with_stdio(false);
}

#line 1 ".lib/math/mod.hpp"



#line 7 ".lib/math/mod.hpp"
#include <type_traits>
#line 9 ".lib/math/mod.hpp"
#include <ostream>
#line 13 ".lib/math/mod.hpp"

// @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;
}
struct barrett {
    unsigned int _m;
    unsigned long long im;
    explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
    unsigned int umod() const { return _m; }
    unsigned int mul(unsigned int a, unsigned int b) const {
        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 long long y = x * _m;
        return (unsigned int)(z - y + (z < y ? _m : 0));
    }
};
// @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;
    constexpr long long bases[3] = {2, 7, 61};
    for (long long a : bases) {
        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);

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);

int ceil_pow2(int n) {
  int x = 0;
  while ((1U << x) < (unsigned int)(n)) x++;
  return x;
}
int bsf(unsigned int n) {
  return __builtin_ctz(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};
    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};
}


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>;


template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : 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>
    static_modint(T v){
        long long x = (long long)(v % (long long)(umod()));
        if (x < 0) x += umod();
        _v = (unsigned int)(x);
    }

    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 = 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 = is_prime<m>;
};

template <int id> struct dynamic_modint : modint_base {
    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 <class T>
    dynamic_modint(T v) {
        long long x = (long long)(v % (long long)(mod()));
        if (x < 0) x += mod();
        _v = (unsigned int)(x);
    }

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

using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
template <class T>
using is_static_modint = std::is_base_of<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>;


template<int m>
std::ostream &operator<<(std::ostream &dest, const static_modint<m> &a){
  dest << a.val();
  return dest;
}

template<int id>
std::ostream &operator<<(std::ostream &dest, const dynamic_modint<id> &a){
  dest << a.val();
  return dest;
}

// 0 <= n < m <= int_max
// 前処理 O(n + log(m))
// 各種計算 O(1)
// 変数 <= n
#line 406 ".lib/math/mod.hpp"
template<typename mint>
struct modcomb{
  private:
    int n;
    std::vector<mint> f, i, fi;
    void init(int _n){
      assert(0 <= _n && _n < mint::mod());
      if(_n < f.size()) return;
      n = _n;
      f.resize(n + 1), i.resize(n + 1), fi.resize(n + 1);
      f[0] = fi[0] = mint(1);
      if(n) f[1] = fi[1] = i[1] = mint(1);
      for(int j = 2; j <= n; j++) f[j] = f[j - 1] * j;
      fi[n] = f[n].inv();
      for(int j = n; j >= 2; j--){
        fi[j - 1] = fi[j] * j;
        i[j] = f[j - 1] * fi[j];
      }
    }
  public:
    modcomb(): n(-1){}
    modcomb(int _n){
      init(_n);
    }
    void recalc(int _n){
      init(std::min(mint::mod() - 1, 1 << ceil_pow2(_n)));
    }
    mint comb(int a, int b){
      if((a < 0) || (b < 0) || (a < b)) return 0;
      return f[a] * fi[a - b] * fi[b];
    }
    mint perm(int a, int b){
      if((a < 0) || (b < 0) || (a < b)) return 0;
      return f[a] * fi[a - b];
    }
    mint fac(int x){
      assert(0 <= x && x <= n);
      return f[x];
    }
    mint inv(int x){
      assert(0 < x && x <= n);
      return i[x];
    }
    mint finv(int x){
      assert(0 <= x && x <= n);
      return fi[x];
    }
};

// mod == 2: 定数時間
// modが素数: O(min(n, mod) + log(n))
template<int id>
struct lucas_prime{
  using mint = dynamic_modint<id>;
  modcomb<mint> mcb;
  void set_mod(int mod){
    mint::set_mod(mod);
  }
  int comb(long long n, long long r){
    if(mint::mod() == 1 || n < 0 || r < 0 || n < r) return 0;
    if(mint::mod() == 2) return (n & r) == r;
    mcb.recalc(std::min(n, (long long)mint::mod()));
    mint res = 1;
    while(n){
      int x = n % mint::mod(), y = r % mint::mod();
      res *= mcb.comb(x, y);
      n /= mint::mod(), r /= mint::mod();
    }
    return res.val();
  }
};

template<typename mint>
struct modpow_table{
  std::vector<mint> v;
  // x^maxkまで計算できる
  modpow_table(){}
  void init(int x, int maxk){
    v.resize(maxk + 1);
    v[0] = 1;
    for(int i = 1; i <= maxk; i++) v[i] = v[i - 1] * x;
  }
  mint pow(int k){
    assert(0 <= k && k < v.size());
    return v[k];
  }
};
template<int m>
int modpow(long long a, long long b){
  int ret = (m == 1 ? 0 : 1), mul = a % m;
  while(b){
    if(b & 1) ret = ((long long)ret * mul) % m;
    mul = ((long long)mul * mul) % m;
    b >>= 1;
  }
  return ret;
}
int modpow(long long a, long long b, int m){
  int ret = (m == 1 ? 0 : 1), mul = a % m;
  while(b){
    if(b & 1) ret = ((long long)ret * mul) % m;
    mul = ((long long)mul * mul) % m;
    b >>= 1;
  }
  return ret;
}

#line 514 ".lib/math/mod.hpp"

// modpow(x,2,mod) == aとなるxを返す
// 存在しないなら-1
// mod は素数
long long modsqrt(long long a, long long mod){
  a %= mod;
	if(a == 0) return 0LL;
	if(mod == 2) return 1LL;
	if(modpow(a, (mod - 1) / 2, mod) != 1) return -1LL;
	if(mod % 4 == 3) return modpow(a, mod / 4 + 1, mod);
	long long q = mod - 1, m = 0;
	while(q % 2 == 0) q >>= 1, m++;
	std::mt19937 mt;
	long long z;
	do{
		z = mt() % mod;
	}while(modpow(z, (mod - 1) / 2, mod) != mod - 1);
	long long c = modpow(z, q, mod);
	long long t = modpow(a, q, mod);
	long long r = modpow(a, (q + 1) >> 1, mod);
	for(; m > 1; --m) {
	  long long tmp = modpow(t, 1LL << (m - 2), mod);
		if(tmp != 1) r = r * c % mod, t = t * (c * c % mod) % mod;
		c = c * c % mod;
	}
	return r;
}

//n次以下の多項式に対し
//f(0) ~ f(n)を与えf(p)を求める
//O(n log(MOD))
template<typename mint>
mint __lagrange(const std::vector<mint> &y, mint p, modcomb<mint> &mcb){
  int sz = y.size();
  mcb.recalc(sz);
  mint M = 1, res = 0;
  std::vector<mint> itable(sz, 1), num(sz);
  if(p.val() < sz) return y[p.val()];
  for(int i = 0; i < sz; i++){
    M *= p - i;
    num[i] = p - i;
  }
  uint32_t cnt = mint::mod() - 2;
  while(cnt){
    if(cnt & 1){
      for(int i = 0; i < sz; i++) itable[i] *= num[i], num[i] *= num[i];
    }else{
      for(int i = 0; i < sz; i++) num[i] *= num[i];
    }
    cnt >>= 1;
  }
  for(int i = 0; i < sz; i++){
    mint iQ = mcb.finv(i) * mcb.finv(sz - 1 - i);
    if((sz - i - 1) & 1) iQ *= -1;
    res += y[i] * iQ * itable[i];
  }
  return res * M;
}
template<typename mint>
mint lagrange(const std::vector<mint> &y, mint p){
  modcomb<mint> mcb;
  return __lagrange(y, p, mcb);
}

template<typename mint>
mint riid(mint r, int d, long long n){
  if(n == 0) return 0;
  if(r.val() == 0){
    return d == 0 ? mint(1) : 0;
  }
  n--;
  std::vector<mint> y(d + 2), ipow(d + 2, 1), tbl(d + 2);
  for(int i = 0; i < d + 2; i++) tbl[i] = i;
  int cnt = d;
  while(cnt){
    if(cnt & 1){
      for(int i = 0; i < d + 2; i++) ipow[i] *= tbl[i], tbl[i] *= tbl[i];
    }else{
      for(int i = 0; i < d + 2; i++) tbl[i] *= tbl[i];
    }
    cnt >>= 1;
  }
  mint tmp = 0, rpow = 1, last = r.pow(n % (mint::mod() - 1));
  n %= mint::mod();
  for(int i = 0; i < d + 2; i++){
    tmp += rpow * ipow[i];
    rpow *= r;
    y[i] = tmp;
  }
  modcomb<mint> mcb(y.size());

  if(r.val() == 1) return __lagrange<mint>(y, n, mcb);
  ipow[0] = 1, ipow[1] = -r;
  mint comb = 1, c = 0;
  for(int i = 2; i < d + 2; i++) ipow[i] = ipow[i - 1] * ipow[1];
  for(int i = 0; i < d + 1; i++){
    comb *= mcb.inv(i + 1) * mint(d + 1 - i);
    c += comb * ipow[d - i] * y[i];
  }
  mint di = mint(1 - r);
  c *= di.pow(d + 1).inv();
  mint powerRinv = 1, rinv = r.inv();
  for(int i = 0; i < d + 1; i++){
    y[i] -= c;
    y[i] *= powerRinv;
    powerRinv *= rinv;
  }
  y.pop_back();
  return c + last * __lagrange<mint>(y, n, mcb);
}


#line 3 "c.cpp"

using mint = modint998244353;

int main(){
  io_init();
  modcomb<mint> mcb(1000000);
  mint ans = 0;
  ll n, m;
  std::cin >> n >> m;
  if(m == 0){
    if(n & 1){
      std::cout << 0 << '\n';
    }else{
      for(int i = 0; i <= (n / 2); i++){
        int j = (n - 2 * i) / 2;
        ans += mcb.comb(n, 2 * i) * mcb.comb(2 * i, i) * mcb.comb(n - 2 * i, j);
      }
      std::cout << ans * mint(4).pow(n) << '\n';
    }
    return 0;
  }
  
  if(m < 0) m *= -1;
  for(ll i = 1; i * i <= m; i++){
    if(m % i != 0) continue;
    ll j = m / i;
    if(i % 2 != j % 2) continue;
    // x - y = i && x + y = j
    // x = (j + i) / 2
    // y = (j - i) / 2

    ll x = (j + i) / 2;
    ll y = (j - i) / 2;

    if(x + y > n || (x + y) % 2 != n % 2) continue;

    mint tmp = 0;
    
    // (+-x, +-y) 4パターン
    // (x, y) を求めて × 4
    for(ll yoko = x; yoko <= n - y; yoko += 2){
      ll tate = n - yoko;
      //std::cout << mcb.comb(n, yoko) << " " << mcb.comb(yoko, x) << '\n';
      tmp += mcb.comb(n, yoko) * mcb.comb(yoko, (yoko - x) / 2) * mcb.comb(tate, (tate - y) / 2);
    }
    if(y == 0) tmp *= 2;
    else tmp *= 4;
    ans += tmp;
  }
  std::cout << (ans / mint(4).pow(n)) << '\n';
}
yukicoder

結果

ソースコード
