結果
問題 | No.802 だいたい等差数列 |
ユーザー |
|
提出日時 | 2022-05-02 18:53:51 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 85 ms / 2,000 ms |
コード長 | 23,434 bytes |
コンパイル時間 | 2,241 ms |
コンパイル使用メモリ | 201,044 KB |
最終ジャッジ日時 | 2025-01-29 01:57:20 |
ジャッジサーバーID (参考情報) |
judge3 / judge5 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 4 |
other | AC * 30 |
ソースコード
/*** author: otera**/#include<bits/stdc++.h>#ifndef OTERA_MODINT#define OTERA_MODINT 1#include <cassert>#include <numeric>#include <type_traits>#ifdef _MSC_VER#include <intrin.h>#endif#include <utility>#ifdef _MSC_VER#include <intrin.h>#endifnamespace atcoder {namespace internal {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_VERunsigned long long x;_umul128(z, im, &x);#elseunsigned long long x =(unsigned long long)(((unsigned __int128)(z)*im) >> 64);#endifunsigned int v = (unsigned int)(z - x * _m);if (_m <= v) v += _m;return v;}};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;}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 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; // |m1 * u| <= |m1| * s <= bauto tmp = s;s = t;t = tmp;tmp = m0;m0 = m1;m1 = tmp;}if (m0 < 0) m0 += b / s;return {s, m0};}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);unsigned long long floor_sum_unsigned(unsigned long long n,unsigned long long m,unsigned long long a,unsigned long long b) {unsigned long long ans = 0;while (true) {if (a >= m) {ans += n * (n - 1) / 2 * (a / m);a %= m;}if (b >= m) {ans += n * (b / m);b %= m;}unsigned long long y_max = a * n + b;if (y_max < m) break;n = (unsigned long long)(y_max / m);b = (unsigned long long)(y_max % m);std::swap(m, a);}return ans;}} // namespace internal} // namespace atcoder#include <cassert>#include <numeric>#include <type_traits>namespace atcoder {namespace internal {#ifndef _MSC_VERtemplate <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;#elsetemplate <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;#endiftemplate <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 atcodernamespace 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 internaltemplate <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());}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());}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 atcodernamespace otera {using modint107 = atcoder::modint1000000007;using modint998 = atcoder::modint998244353;using modint = atcoder::modint;}; //namespace oterastd::ostream& operator<<(std::ostream& out, const atcoder::modint1000000007 &e) {out << e.val();return out;}std::ostream& operator<<(std::ostream& out, const atcoder::modint998244353 &e) {out << e.val();return out;}std::ostream& operator<<(std::ostream& out, const atcoder::modint &e) {out << e.val();return out;}#endif // OTERA_MODINT// #include<otera/Factorial>using namespace std;#define int long longusing ll = long long;using ld = long double;using ull = unsigned long long;using int128_t = __int128_t;#define repa(i, n) for(int i = 0; i < n; ++ i)#define repb(i, a, b) for(int i = a; i < b; ++ i)#define repc(i, a, b, c) for(int i = a; i < b; i += c)#define overload4(a, b, c, d, e, ...) e#define overload3(a, b, c, d, ...) d#define rep(...) overload4(__VA_ARGS__, repc, repb, repa)(__VA_ARGS__)#define rep1a(i, n) for(int i = 0; i <= n; ++ i)#define rep1b(i, a, b) for(int i = a; i <= b; ++ i)#define rep1c(i, a, b, c) for(int i = a; i <= b; i += c)#define rep1(...) overload4(__VA_ARGS__, rep1c, rep1b, rep1a)(__VA_ARGS__)#define rev_repa(i, n) for(int i=n-1;i>=0;i--)#define rev_repb(i, a, b) assert(a > b);for(int i=a;i>b;i--)#define rev_rep(...) overload3(__VA_ARGS__, rev_repb, rev_repa)(__VA_ARGS__)#define rev_rep1a(i, n) for(int i=n;i>=1;i--)#define rev_rep1b(i, a, b) assert(a >= b);for(int i=a;i>=b;i--)#define rev_rep1(...) overload3(__VA_ARGS__, rev_rep1b, rev_rep1a)(__VA_ARGS__)typedef pair<int, int> P;typedef pair<ll, ll> LP;#define pb push_back#define pf push_front#define ppb pop_back#define ppf pop_front#define eb emplace_back#define fr first#define sc second#define all(c) c.begin(),c.end()#define rall(c) c.rbegin(), c.rend()#define lb(c, x) distance((c).begin(), lower_bound(all(c), (x)))#define ub(c, x) distance((c).begin(), upper_bound(all(c), (x)))#define Sort(a) sort(all(a))#define Rev(a) reverse(all(a))#define Uniq(a) sort(all(a));a.erase(unique(all(a)),end(a))#define si(c) (int)(c).size()inline ll popcnt(ull a){ return __builtin_popcountll(a); }#define kth_bit(x, k) ((x>>k)&1)#define unless(A) if(!(A))ll intpow(ll a, ll b){ ll ans = 1; while(b){ if(b & 1) ans *= a; a *= a; b /= 2; } return ans; }ll intpow(ll a, ll b, ll m) {ll ans = 1; while(b){ if(b & 1) (ans *= a) %= m; (a *= a) %= m; b /= 2; } return ans; }template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }#define INT(...) int __VA_ARGS__;in(__VA_ARGS__)#define LL(...) ll __VA_ARGS__;in(__VA_ARGS__)#define ULL(...) ull __VA_ARGS__;in(__VA_ARGS__)#define STR(...) string __VA_ARGS__;in(__VA_ARGS__)#define CHR(...) char __VA_ARGS__;in(__VA_ARGS__)#define DBL(...) double __VA_ARGS__;in(__VA_ARGS__)#define LD(...) ld __VA_ARGS__;in(__VA_ARGS__)#define vec(type,name,...) vector<type>name(__VA_ARGS__)#define VEC(type,name,size) vector<type>name(size);in(name)#define vv(type,name,h,...) vector<vector<type>>name(h,vector<type>(__VA_ARGS__))#define VV(type,name,h,w) vector<vector<type>>name(h,vector<type>(w));in(name)#define vvv(type,name,h,w,...) vector<vector<vector<type>>>name(h,vector<vector<type>>(w,vector<type>(__VA_ARGS__)))template <class T> using vc = vector<T>;template <class T> using vvc = vector<vc<T>>;template <class T> using vvvc = vector<vvc<T>>;template <class T> using vvvvc = vector<vvvc<T>>;template <class T> using pq = priority_queue<T>;template <class T> using pqg = priority_queue<T, vector<T>, greater<T>>;template <class T, class U> using umap = unordered_map<T, U>;template<class T> void scan(T& a){ cin >> a; }template<class T> void scan(vector<T>& a){ for(auto&& i : a) scan(i); }void in(){}template <class Head, class... Tail> void in(Head& head, Tail&... tail){ scan(head); in(tail...); }void print(){ cout << ' '; }template<class T> void print(const T& a){ cout << a; }template<class T> void print(const vector<T>& a){ if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ cout << ' '; print(*i); } }int out(){ cout << '\n'; return 0; }template<class T> int out(const T& t){ print(t); cout << '\n'; return 0; }template<class Head, class... Tail> int out(const Head& head, const Tail&... tail){ print(head); cout << ' '; out(tail...); return 0; }#define CHOOSE(a) CHOOSE2 a#define CHOOSE2(a0,a1,a2,a3,a4,x,...) x#define debug_1(x1) cout<<#x1<<": "<<x1<<endl#define debug_2(x1,x2) cout<<#x1<<": "<<x1<<", "#x2<<": "<<x2<<endl#define debug_3(x1,x2,x3) cout<<#x1<<": "<<x1<<", "#x2<<": "<<x2<<", "#x3<<": "<<x3<<endl#define debug_4(x1,x2,x3,x4) cout<<#x1<<": "<<x1<<", "#x2<<": "<<x2<<", "#x3<<": "<<x3<<", "#x4<<": "<<x4<<endl#define debug_5(x1,x2,x3,x4,x5) cout<<#x1<<": "<<x1<<", "#x2<<": "<<x2<<", "#x3<<": "<<x3<<", "#x4<<": "<<x4<<", "#x5<<": "<<x5<<endl#ifdef DEBUG#define debug(...) CHOOSE((__VA_ARGS__,debug_5,debug_4,debug_3,debug_2,debug_1,~))(__VA_ARGS__)#define dump(...) { print(#__VA_ARGS__); print(":"); out(__VA_ARGS__); }#else#define debug(...)#define dump(...)#endifstruct io_setup {io_setup(int precision = 20) {ios::sync_with_stdio(false);cin.tie(0);cout << fixed << setprecision(precision);}} io_setup_ {};using mint = otera::modint107;// otera::factorial<mint> bc;// modint: mod 計算を int を扱うように扱える構造体template<int MOD> struct Fp {long long val;constexpr Fp(long long v = 0) noexcept : val(v % MOD) {if (val < 0) val += MOD;}constexpr int getmod() { return MOD; }constexpr Fp operator - () const noexcept {return val ? MOD - val : 0;}constexpr Fp operator + (const Fp& r) const noexcept { return Fp(*this) += r; }constexpr Fp operator - (const Fp& r) const noexcept { return Fp(*this) -= r; }constexpr Fp operator * (const Fp& r) const noexcept { return Fp(*this) *= r; }constexpr Fp operator / (const Fp& r) const noexcept { return Fp(*this) /= r; }constexpr Fp& operator += (const Fp& r) noexcept {val += r.val;if (val >= MOD) val -= MOD;return *this;}constexpr Fp& operator -= (const Fp& r) noexcept {val -= r.val;if (val < 0) val += MOD;return *this;}constexpr Fp& operator *= (const Fp& r) noexcept {val = val * r.val % MOD;return *this;}constexpr Fp& operator /= (const Fp& r) noexcept {long long a = r.val, b = MOD, u = 1, v = 0;while (b) {long long t = a / b;a -= t * b; swap(a, b);u -= t * v; swap(u, v);}val = val * u % MOD;if (val < 0) val += MOD;return *this;}constexpr bool operator == (const Fp& r) const noexcept {return this->val == r.val;}constexpr bool operator != (const Fp& r) const noexcept {return this->val != r.val;}friend constexpr ostream& operator << (ostream &os, const Fp<MOD>& x) noexcept {return os << x.val;}friend constexpr istream& operator >> (istream &is, Fp<MOD>& x) noexcept {return is >> x.val;}friend constexpr Fp<MOD> modpow(const Fp<MOD> &a, long long n) noexcept {if (n == 0) return 1;auto t = modpow(a, n / 2);t = t * t;if (n & 1) t = t * a;return t;}};template<class T> struct BiCoef {vector<T> fact_, inv_, finv_;int MOD = T::mod();constexpr BiCoef() {}constexpr BiCoef(int n) noexcept : fact_(n, 1), inv_(n, 1), finv_(n, 1) {init(n);}constexpr void init(int n) noexcept {fact_.assign(n, 1), inv_.assign(n, 1), finv_.assign(n, 1);for(int i = 2; i < n; i++){fact_[i] = fact_[i-1] * i;inv_[i] = -inv_[MOD%i] * (MOD/i);finv_[i] = finv_[i-1] * inv_[i];}}constexpr T com(int n, int k) const noexcept {if(n == k) return 1;if (n < k || n < 0 || k < 0) return 0;return fact_[n] * finv_[k] * finv_[n-k];}constexpr T fact(int n) const noexcept {if (n < 0) return 0;return fact_[n];}constexpr T inv(int n) const noexcept {if (n < 0) return 0;return inv_[n];}constexpr T finv(int n) const noexcept {if (n < 0) return 0;return finv_[n];}};BiCoef<mint> bc;void solve() {bc.init(1400100);INT(n, m);VEC(int, d, 2);int t = d[1] - d[0];int sum = (m - 1) - (n - 1) * d[0];debug(t, sum);mint ans = 0;for(int i = 0; i <= n - 1; ++ i) {mint val = bc.com(n - 1, i) * bc.com(sum - (t + 1) * i + n, n);if(i % 2 == 0) ans += val;else ans -= val;}out(ans);}signed main() {int testcase = 1;// in(testcase);while(testcase--) solve();return 0;}