結果
| 問題 | No.1919 Many Monster Battles |
| ユーザー |
 suisen
|
| 提出日時 | 2022-04-30 00:05:36 |
| 言語 | C++17 (gcc 13.2.0 + boost 1.83.0) |
| 結果 |
CE
(最新)
AC
(最初)
|
| 実行時間 | - |
| コード長 | 37,209 bytes |
| コンパイル時間 | 2,962 ms |
| コンパイル使用メモリ | 225,320 KB |
| 最終ジャッジ日時 | 2023-08-08 20:13:06 |
| 合計ジャッジ時間 | 6,367 ms |
|
ジャッジサーバーID （参考情報） |
judge15 / judge13 |
コンパイルエラー時のメッセージ・ソースコードは、提出者また管理者しか表示できないようにしております。（リジャッジ後のコンパイルエラーは公開されます）
ただし、clay言語の場合は開発者のデバッグのため、公開されます。
ただし、clay言語の場合は開発者のデバッグのため、公開されます。
コンパイルメッセージ
main.cpp: In instantiation of ‘std::ostream& operator<<(std::ostream&, const std::vector<_Tp>&) [with T = atcoder::static_modint<1000000007>; std::ostream = std::basic_ostream<char>]’:
main.cpp:151:15: required from ‘void print(const Head&, const Tail& ...) [with Head = std::vector<atcoder::static_modint<1000000007> >; Tail = {}]’
main.cpp:1197:10: required from here
main.cpp:134:13: エラー: no match for ‘operator<<’ (operand types are ‘std::ostream’ {aka ‘std::basic_ostream<char>’} and ‘const atcoder::static_modint<1000000007>’)
134 | out << *it;
| ~~~~^~~~~~
次のファイルから読み込み: /usr/local/gcc7/include/c++/12.2.0/istream:39,
次から読み込み: /usr/local/gcc7/include/c++/12.2.0/sstream:38,
次から読み込み: /usr/local/gcc7/include/c++/12.2.0/complex:45,
次から読み込み: /usr/local/gcc7/include/c++/12.2.0/ccomplex:39,
次から読み込み: /usr/local/gcc7/include/c++/12.2.0/x86_64-pc-linux-gnu/bits/stdc++.h:54,
次から読み込み: main.cpp:7:
/usr/local/gcc7/include/c++/12.2.0/ostream:108:7: 備考: 候補: ‘std::basic_ostream<_CharT, _Traits>::__ostream_type& std::basic_ostream<_CharT, _Traits>::operator<<(__ostream_type& (*)(__ostream_type&)) [with _CharT = char; _Traits = std::char_traits<char>; __ostream_type = std::basic_ostream<char>]’
108 | operator<<(__ostream_type& (*__pf)(__ostream_type&))
| ^~~~~~~~
/usr/local/gcc7/include/c++/12.2.0/ostream:108:36: 備考: no known conversion for argument 1 from ‘const atcoder::static_modint<1000000007>’ to ‘std::basic_ostream<char>::__ostream_type& (*)(std::basic_ostream<char>::__ostream_type&)’ {aka ‘std::basic_ostream<char>& (*)(std::basic_ostream<char>&)’}
108 | operator<<(__ostream_type& (*__pf)(__ostream_type&))
| ~~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~
/usr/local/gcc7/include/c++/12.2.0/ostream:117:7: 備
ソースコード
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
// #pragma comment(linker, "/stack:200000000")
#include <bits/stdc++.h>
#include <limits>
#include <type_traits>
namespace suisen {
// ! utility
template <typename ...Types>
using constraints_t = std::enable_if_t<std::conjunction_v<Types...>, std::nullptr_t>;
template <bool cond_v, typename Then, typename OrElse>
constexpr decltype(auto) constexpr_if(Then&& then, OrElse&& or_else) {
if constexpr (cond_v) {
return std::forward<Then>(then);
} else {
return std::forward<OrElse>(or_else);
}
}
// ! function
template <typename ReturnType, typename Callable, typename ...Args>
using is_same_as_invoke_result = std::is_same<std::invoke_result_t<Callable, Args...>, ReturnType>;
template <typename F, typename T>
using is_uni_op = is_same_as_invoke_result<T, F, T>;
template <typename F, typename T>
using is_bin_op = is_same_as_invoke_result<T, F, T, T>;
template <typename Comparator, typename T>
using is_comparator = std::is_same<std::invoke_result_t<Comparator, T, T>, bool>;
// ! integral
template <typename T, typename = constraints_t<std::is_integral<T>>>
constexpr int bit_num = std::numeric_limits<std::make_unsigned_t<T>>::digits;
template <typename T, unsigned int n>
struct is_nbit { static constexpr bool value = bit_num<T> == n; };
template <typename T, unsigned int n>
static constexpr bool is_nbit_v = is_nbit<T, n>::value;
// ?
template <typename T>
struct safely_multipliable {};
template <>
struct safely_multipliable<int> { using type = long long; };
template <>
struct safely_multipliable<long long> { using type = __int128_t; };
template <>
struct safely_multipliable<unsigned int> { using type = unsigned long long; };
template <>
struct safely_multipliable<unsigned long long> { using type = __uint128_t; };
template <>
struct safely_multipliable<float> { using type = float; };
template <>
struct safely_multipliable<double> { using type = double; };
template <>
struct safely_multipliable<long double> { using type = long double; };
template <typename T>
using safely_multipliable_t = typename safely_multipliable<T>::type;
} // namespace suisen
// ! type aliases
using i128 = __int128_t;
using u128 = __uint128_t;
using ll = long long;
using uint = unsigned int;
using ull = unsigned long long;
template <typename T> using vec = std::vector<T>;
template <typename T> using vec2 = vec<vec <T>>;
template <typename T> using vec3 = vec<vec2<T>>;
template <typename T> using vec4 = vec<vec3<T>>;
template <typename T>
using pq_greater = std::priority_queue<T, std::vector<T>, std::greater<T>>;
template <typename T, typename U>
using umap = std::unordered_map<T, U>;
// ! macros (capital: internal macro)
#define OVERLOAD2(_1,_2,name,...) name
#define OVERLOAD3(_1,_2,_3,name,...) name
#define OVERLOAD4(_1,_2,_3,_4,name,...) name
#define REP4(i,l,r,s) for(std::remove_reference_t<std::remove_const_t<decltype(r)>>i=(l);i<(r);i+=(s))
#define REP3(i,l,r) REP4(i,l,r,1)
#define REP2(i,n) REP3(i,0,n)
#define REPINF3(i,l,s) for(std::remove_reference_t<std::remove_const_t<decltype(l)>>i=(l);;i+=(s))
#define REPINF2(i,l) REPINF3(i,l,1)
#define REPINF1(i) REPINF2(i,0)
#define RREP4(i,l,r,s) for(std::remove_reference_t<std::remove_const_t<decltype(r)>>i=(l)+fld((r)-(l)-1,s)*(s);i>=(l);i-=(s))
#define RREP3(i,l,r) RREP4(i,l,r,1)
#define RREP2(i,n) RREP3(i,0,n)
#define rep(...) OVERLOAD4(__VA_ARGS__, REP4 , REP3 , REP2 )(__VA_ARGS__)
#define rrep(...) OVERLOAD4(__VA_ARGS__, RREP4 , RREP3 , RREP2 )(__VA_ARGS__)
#define repinf(...) OVERLOAD3(__VA_ARGS__, REPINF3, REPINF2, REPINF1)(__VA_ARGS__)
#define CAT_I(a, b) a##b
#define CAT(a, b) CAT_I(a, b)
#define UNIQVAR(tag) CAT(tag, __LINE__)
#define loop(n) for (std::remove_reference_t<std::remove_const_t<decltype(n)>> UNIQVAR(loop_variable) = n; UNIQVAR(loop_variable) --> 0;)
#define all(iterable) (iterable).begin(), (iterable).end()
#define input(type, ...) type __VA_ARGS__; read(__VA_ARGS__)
// ! I/O utilities
// pair
template <typename T, typename U>
std::ostream& operator<<(std::ostream& out, const std::pair<T, U> &a) {
return out << a.first << ' ' << a.second;
}
// tuple
template <unsigned int N = 0, typename ...Args>
std::ostream& operator<<(std::ostream& out, const std::tuple<Args...> &a) {
if constexpr (N >= std::tuple_size_v<std::tuple<Args...>>) {
return out;
} else {
out << std::get<N>(a);
if constexpr (N + 1 < std::tuple_size_v<std::tuple<Args...>>) {
out << ' ';
}
return operator<<<N + 1>(out, a);
}
}
// vector
template <typename T>
std::ostream& operator<<(std::ostream& out, const std::vector<T> &a) {
for (auto it = a.begin(); it != a.end();) {
out << *it;
if (++it != a.end()) out << ' ';
}
return out;
}
// array
template <typename T, size_t N>
std::ostream& operator<<(std::ostream& out, const std::array<T, N> &a) {
for (auto it = a.begin(); it != a.end();) {
out << *it;
if (++it != a.end()) out << ' ';
}
return out;
}
inline void print() { std::cout << '\n'; }
template <typename Head, typename... Tail>
inline void print(const Head &head, const Tail &...tails) {
std::cout << head;
if (sizeof...(tails)) std::cout << ' ';
print(tails...);
}
template <typename Iterable>
auto print_all(const Iterable& v, std::string sep = " ", std::string end = "\n") -> decltype(std::cout << *v.begin(), void()) {
for (auto it = v.begin(); it != v.end();) {
std::cout << *it;
if (++it != v.end()) std::cout << sep;
}
std::cout << end;
}
// pair
template <typename T, typename U>
std::istream& operator>>(std::istream& in, std::pair<T, U> &a) {
return in >> a.first >> a.second;
}
// tuple
template <unsigned int N = 0, typename ...Args>
std::istream& operator>>(std::istream& in, std::tuple<Args...> &a) {
if constexpr (N >= std::tuple_size_v<std::tuple<Args...>>) {
return in;
} else {
return operator>><N + 1>(in >> std::get<N>(a), a);
}
}
// vector
template <typename T>
std::istream& operator>>(std::istream& in, std::vector<T> &a) {
for (auto it = a.begin(); it != a.end(); ++it) in >> *it;
return in;
}
// array
template <typename T, size_t N>
std::istream& operator>>(std::istream& in, std::array<T, N> &a) {
for (auto it = a.begin(); it != a.end(); ++it) in >> *it;
return in;
}
template <typename ...Args>
void read(Args &...args) {
( std::cin >> ... >> args );
}
// ! integral utilities
// Returns pow(-1, n)
template <typename T>
constexpr inline int pow_m1(T n) {
return -(n & 1) | 1;
}
// Returns pow(-1, n)
template <>
constexpr inline int pow_m1<bool>(bool n) {
return -int(n) | 1;
}
// Returns floor(x / y)
template <typename T>
constexpr inline T fld(const T x, const T y) {
return (x ^ y) >= 0 ? x / y : (x - (y + pow_m1(y >= 0))) / y;
}
template <typename T>
constexpr inline T cld(const T x, const T y) {
return (x ^ y) <= 0 ? x / y : (x + (y + pow_m1(y >= 0))) / y;
}
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 16>> = nullptr>
constexpr inline int popcount(const T x) { return __builtin_popcount(x); }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 32>> = nullptr>
constexpr inline int popcount(const T x) { return __builtin_popcount(x); }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 64>> = nullptr>
constexpr inline int popcount(const T x) { return __builtin_popcountll(x); }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 16>> = nullptr>
constexpr inline int count_lz(const T x) { return x ? __builtin_clz(x) : suisen::bit_num<T>; }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 32>> = nullptr>
constexpr inline int count_lz(const T x) { return x ? __builtin_clz(x) : suisen::bit_num<T>; }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 64>> = nullptr>
constexpr inline int count_lz(const T x) { return x ? __builtin_clzll(x) : suisen::bit_num<T>; }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 16>> = nullptr>
constexpr inline int count_tz(const T x) { return x ? __builtin_ctz(x) : suisen::bit_num<T>; }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 32>> = nullptr>
constexpr inline int count_tz(const T x) { return x ? __builtin_ctz(x) : suisen::bit_num<T>; }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 64>> = nullptr>
constexpr inline int count_tz(const T x) { return x ? __builtin_ctzll(x) : suisen::bit_num<T>; }
template <typename T>
constexpr inline int floor_log2(const T x) { return suisen::bit_num<T> - 1 - count_lz(x); }
template <typename T>
constexpr inline int ceil_log2(const T x) { return floor_log2(x) + ((x & -x) != x); }
template <typename T>
constexpr inline int kth_bit(const T x, const unsigned int k) { return (x >> k) & 1; }
template <typename T>
constexpr inline int parity(const T x) { return popcount(x) & 1; }
struct all_subset {
struct all_subset_iter {
const int s; int t;
constexpr all_subset_iter(int s) : s(s), t(s + 1) {}
constexpr auto operator*() const { return t; }
constexpr auto operator++() {}
constexpr auto operator!=(std::nullptr_t) { return t ? (--t &= s, true) : false; }
};
int s;
constexpr all_subset(int s) : s(s) {}
constexpr auto begin() { return all_subset_iter(s); }
constexpr auto end() { return nullptr; }
};
// ! container
template <typename T, typename Comparator, suisen::constraints_t<suisen::is_comparator<Comparator, T>> = nullptr>
auto priqueue_comp(const Comparator comparator) {
return std::priority_queue<T, std::vector<T>, Comparator>(comparator);
}
template <typename Iterable>
auto isize(const Iterable &iterable) -> decltype(int(iterable.size())) {
return iterable.size();
}
template <typename T, typename Gen, suisen::constraints_t<suisen::is_same_as_invoke_result<T, Gen, int>> = nullptr>
auto generate_vector(int n, Gen generator) {
std::vector<T> v(n);
for (int i = 0; i < n; ++i) v[i] = generator(i);
return v;
}
template <typename T>
auto generate_range_vector(T l, T r) {
return generate_vector(r - l, [l](int i) { return l + i; });
}
template <typename T>
auto generate_range_vector(T n) {
return generate_range_vector(0, n);
}
template <typename T>
void sort_unique_erase(std::vector<T> &a) {
std::sort(a.begin(), a.end());
a.erase(std::unique(a.begin(), a.end()), a.end());
}
template <typename InputIterator, typename BiConsumer>
auto foreach_adjacent_values(InputIterator first, InputIterator last, BiConsumer f) -> decltype(f(*first++, *last), void()) {
if (first != last) for (auto itr = first, itl = itr++; itr != last; itl = itr++) f(*itl, *itr);
}
template <typename Container, typename BiConsumer>
auto foreach_adjacent_values(Container c, BiConsumer f) -> decltype(c.begin(), c.end(), void()){
foreach_adjacent_values(c.begin(), c.end(), f);
}
// ! other utilities
// x <- min(x, y). returns true iff `x` has chenged.
template <typename T>
inline bool chmin(T &x, const T &y) {
if (y >= x) return false;
x = y;
return true;
}
// x <- max(x, y). returns true iff `x` has chenged.
template <typename T>
inline bool chmax(T &x, const T &y) {
if (y <= x) return false;
x = y;
return true;
}
namespace suisen {}
using namespace suisen;
using namespace std;
struct io_setup {
io_setup(int precision = 20) {
std::ios::sync_with_stdio(false);
std::cin.tie(nullptr);
std::cout << std::fixed << std::setprecision(precision);
}
} io_setup_{};
// ! code from here
#include <cassert>
#include <numeric>
#ifdef _MSC_VER
#include <intrin.h>
#endif
#include <utility>
#ifdef _MSC_VER
#endif
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 modular multiplication 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 < 2^31`
explicit 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;
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);
// @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);
// @param n `n < 2^32`
// @param m `1 <= m < 2^32`
// @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)
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;
// y_max < m * (n + 1)
// floor(y_max / m) <= n
n = (unsigned long long)(y_max / m);
b = (unsigned long long)(y_max % m);
std::swap(m, a);
}
return ans;
}
} // namespace internal
} // namespace atcoder
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
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());
}
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 atcoder
using mint = atcoder::modint1000000007;
std::istream& operator>>(std::istream& in, mint& a) {
long long e; in >> e; a = e;
return in;
}
std::ostream& operator<<(std::ostream& out, const mint& a) {
out << a.val();
return out;
}
#include <algorithm>
#include <vector>
namespace suisen {
struct Permutation : public std::vector<int> {
using base_type = std::vector<int>;
using base_type::base_type;
Permutation() : Permutation(0) {}
Permutation(std::size_t n) : Permutation(int(n)) {}
Permutation(int n) : base_type(n) {
std::iota(begin(), end(), 0);
}
Permutation(const std::vector<int>& a) : std::vector<int>(a) {}
Permutation(std::vector<int>&& a) : std::vector<int>(std::move(a)) {}
// returns b s.t. b[i] = a[p[i]]
template <typename T>
std::vector<T> permute(const std::vector<T>& a) const {
const int n = a.size();
std::vector<T> res(n);
for (int i = 0; i < n; ++i) res[i] = a[(*this)[i]];
return res;
}
// returns b s.t. b[p[i]] = a[i]
template <typename T>
std::vector<T> inv_permute(const std::vector<T>& a) const {
const int n = a.size();
std::vector<T> res(n);
for (int i = 0; i < n; ++i) res[(*this)[i]] = a[i];
return res;
}
// returns p * q s.t. (p * q)[i] = p[q[i]]
friend Permutation operator*(const Permutation& p, const Permutation& q) {
return q.permute(p);
}
Permutation& operator*=(const Permutation& q) {
return *this = *this * q;
}
Permutation inv() const {
const int n = size();
Permutation res(n);
for (int i = 0; i < n; ++i) res[(*this)[i]] = i;
return res;
}
Permutation pow(long long k) const {
assert(k >= 0);
const int n = size();
std::vector<int8_t> seen(n, false);
Permutation res(n);
for (int s = 0; s < n; ++s) {
if (seen[s]) continue;
std::vector<int> cycle { s };
for (int v = (*this)[s]; v != s; v = (*this)[v]) cycle.push_back(v);
const int l = cycle.size();
for (int j = 0; j < l; ++j) {
int v = cycle[j];
seen[v] = true;
res[v] = cycle[(j + k) % l];
}
}
return res;
}
template <typename T, typename Comp = std::less<T>>
static Permutation index_sort(const std::vector<T>& a, Comp comp = Comp{}) {
Permutation p(a.size());
std::sort(p.begin(), p.end(), [&](int i, int j) { return comp(a[i], a[j]); });
return p;
}
};
template <typename hash_t>
struct PermutationHash {
hash_t operator()(const Permutation &p) const {
return hash(p);
}
/**
* minimal perfect hash function for permutations.
* complexity: O(n) time, O(n) extra space
* reference: https://twitter.com/noshi91/status/1452081886025555972?s=20
*/
static hash_t hash(const Permutation &per) {
hash_t h = 0;
const int n = per.size();
Permutation p = per;
Permutation q = per.inv();
for (int i = n - 1; i >= 0; --i) {
h = h * (i + 1) + p[i];
p[q[i]] = p[i];
q[p[i]] = q[i];
}
return h;
}
static Permutation unhash(int n, hash_t h) {
Permutation p = Permutation(n), q = p;
for (int i = 0; i < n; ++i) {
p[i] = h % (i + 1), q[i] = q[p[i]];
q[p[i]] = p[q[i]] = i;
h /= i + 1;
}
return p;
}
};
} // namespace suisen
namespace suisen {
template <typename T, typename U>
std::pair<T, U>& operator+=(std::pair<T, U> &p1, const std::pair<T, U> &p2) {
p1.first += p2.first, p1.second += p2.second;
return p1;
}
template <typename T, typename U>
std::pair<T, U> operator+(const std::pair<T, U> &p1, const std::pair<T, U> &p2) {
return {p1.first + p2.first, p1.second + p2.second};
}
template <typename T, typename U>
std::pair<T, U>& operator-=(std::pair<T, U> &p1, const std::pair<T, U> &p2) {
p1.first -= p2.first, p1.second -= p2.second;
return p1;
}
template <typename T, typename U>
std::pair<T, U> operator-(const std::pair<T, U> &p1, const std::pair<T, U> &p2) {
return {p1.first - p2.first, p1.second - p2.second};
}
template <typename T, typename U, typename V>
std::pair<T, U>& operator*=(std::pair<T, U> &p, const V m) {
p.first *= m, p.second *= m;
return p;
}
template <typename T, typename U, typename V>
std::pair<T, U> operator*(const std::pair<T, U> &p, const V m) {
return {p.first * m, p.second * m};
}
template <typename T, typename U, typename V>
std::pair<T, U> operator*(const V m, const std::pair<T, U> &p) {
return {p.first * m, p.second * m};
}
} // namespace suisen
using S = pair<int, mint>;
struct FenwickTree1D {
int N;
vector<S> BIT;
FenwickTree1D(int N, S qdef = S{}) : N(N), BIT(N + 1, qdef) {}
template <class F>
FenwickTree1D(int N, F f, S qdef = S{}) : FenwickTree1D(N, qdef) {
for (int i = 1; i <= N; i++) {
BIT[i] += f();
int j = i + (i & -i);
if (j <= N) BIT[j] += BIT[i];
}
}
template <class It>
FenwickTree1D(It st, It en, S qdef = S{}) : FenwickTree1D(en - st, [&] { return *st++; }, qdef) {}
vector<S> values() {
vector<S> ret(BIT.begin() + 1, BIT.end());
for (int i = N; i >= 1; i--) {
int j = i + (i & -i);
if (j <= N) ret[j - 1] -= ret[i - 1];
}
return ret;
}
void update(int i, S v) {
for (i++; i <= N; i += i & -i) BIT[i] += v;
}
S query(int r) {
S ret = BIT[0];
for (r++; r > 0; r -= r & -r) ret += BIT[r];
return ret;
}
S query(int l, int r) {
return query(r) - query(l - 1);
}
};
// add (x, y, v)
// query [x1, x2] x [y1, y2]
struct Query {
int t, xlo, xhi, ylo, yhi;
S v;
Query(int t, int xlo, int xhi, int ylo, int yhi, S v) : t(t), xlo(xlo), xhi(xhi), ylo(ylo), yhi(yhi), v(v) {}
};
void add_point(vector<Query>& queries, int x, int y, S v) { queries.push_back(Query(0, x, x, y, y, v)); }
void add_query(vector<Query>& queries, int l, int d, int r, int u) { queries.push_back(Query(1, l, r, d, u, S{})); }
struct Event {
int t, x, ylo, yhi;
S v;
Event(int t, int x, int ylo, int yhi, S v) : t(t), x(x), ylo(ylo), yhi(yhi), v(v) {}
bool operator<(const Event& e) const { return make_pair(x, t) < make_pair(e.x, e.t); }
};
vector<S> solve(vector<Query> queries) {
vector<Event> events;
events.reserve(queries.size() * 2);
vector<int> YS;
YS.reserve(queries.size());
for (auto&& q : queries)
if (q.t == 0)
YS.push_back(q.ylo);
sort(YS.begin(), YS.end());
YS.erase(unique(YS.begin(), YS.end()), YS.end());
int qcnt = 0;
for (auto&& q : queries) {
if (q.t == 0)
q.ylo = lower_bound(YS.begin(), YS.end(), q.ylo) - YS.begin();
else {
q.ylo = lower_bound(YS.begin(), YS.end(), q.ylo) - YS.begin();
q.yhi = int(upper_bound(YS.begin(), YS.end(), q.yhi) - YS.begin()) - 1;
q.v.first = qcnt++;
if (q.ylo > q.yhi) q.t = -1;
}
}
vector<S> ans(qcnt);
FenwickTree1D FT(YS.size());
function<void(int, int)> rec = [&](int l, int r) {
if (l == r)
return;
int m = l + (r - l) / 2;
rec(l, m);
rec(m + 1, r);
events.clear();
for (int i = l; i <= m; i++)
if (queries[i].t == 0)
events.emplace_back(0, queries[i].xlo, queries[i].ylo, queries[i].ylo, queries[i].v);
if (events.empty())
return;
int curSize = events.size();
for (int i = m + 1; i <= r; i++)
if (queries[i].t == 1) {
events.emplace_back(-1, queries[i].xlo, queries[i].ylo, queries[i].yhi, queries[i].v);
events.emplace_back(1, queries[i].xhi, queries[i].ylo, queries[i].yhi, queries[i].v);
}
if (curSize == int(events.size()))
return;
sort(events.begin(), events.end());
for (auto&& e : events) {
if (e.t == 0)
FT.update(e.ylo, e.v);
else
ans[e.v.first] += e.t * FT.query(e.ylo, e.yhi);
}
for (auto&& e : events)
if (e.t == 0)
FT.update(e.ylo, { -e.v.first, -e.v.second });
};
if (qcnt > 0)
rec(0, int(queries.size()) - 1);
return ans;
}
constexpr int inf = numeric_limits<int>::max() - 10;
int main() {
input(int, n);
vector<int> x(n), y(n);
read(x, y);
vector<mint> answers;
loop(2) {
auto p = Permutation::index_sort(x);
x = p.permute(x);
y = p.permute(y);
vector<Query> queries;
mint ans = 0;
rep(i, n) {
int u = x[i] - y[i];
int v = x[i] + y[i];
add_query(queries, -inf, -inf, u - 1, v - 1);
add_point(queries, u, v, { 1, x[i] });
}
int i = 0;
for (auto [num, sum] : solve(queries)) {
ans += mint(num) * x[i++] - sum;
}
answers.push_back(ans * 2);
x.swap(y);
}
print(answers);
return 0;
}