結果
| 問題 | No.1919 Many Monster Battles |
| ユーザー |
 maspy
|
| 提出日時 | 2024-07-20 01:15:04 |
| 言語 | C++23 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 45,157 bytes |
| コンパイル時間 | 6,857 ms |
| コンパイル使用メモリ | 342,316 KB |
| 実行使用メモリ | 52,432 KB |
| 最終ジャッジ日時 | 2024-07-20 01:15:54 |
| 合計ジャッジ時間 | 47,443 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge2 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 2 ms
5,248 KB |
| testcase_01 | AC | 2 ms
5,376 KB |
| testcase_02 | AC | 2 ms
5,376 KB |
| testcase_03 | AC | 5 ms
5,376 KB |
| testcase_04 | AC | 5 ms
5,376 KB |
| testcase_05 | AC | 5 ms
5,376 KB |
| testcase_06 | AC | 5 ms
5,376 KB |
| testcase_07 | AC | 5 ms
5,376 KB |
| testcase_08 | AC | 10 ms
5,376 KB |
| testcase_09 | AC | 5 ms
5,376 KB |
| testcase_10 | AC | 5 ms
5,376 KB |
| testcase_11 | AC | 5 ms
5,376 KB |
| testcase_12 | AC | 5 ms
5,376 KB |
| testcase_13 | TLE | - |
| testcase_14 | TLE | - |
| testcase_15 | TLE | - |
| testcase_16 | TLE | - |
| testcase_17 | TLE | - |
| testcase_18 | TLE | - |
| testcase_19 | TLE | - |
| testcase_20 | TLE | - |
| testcase_21 | TLE | - |
| testcase_22 | TLE | - |
| testcase_23 | AC | 1,047 ms
52,304 KB |
| testcase_24 | AC | 1,042 ms
52,304 KB |
| testcase_25 | AC | 1,044 ms
52,300 KB |
| testcase_26 | AC | 1,045 ms
52,432 KB |
| testcase_27 | AC | 967 ms
52,300 KB |
| testcase_28 | AC | 968 ms
52,304 KB |
| testcase_29 | AC | 970 ms
52,356 KB |
| testcase_30 | AC | 969 ms
52,296 KB |
| testcase_31 | AC | 1,748 ms
52,304 KB |
| testcase_32 | AC | 1,785 ms
52,300 KB |
| testcase_33 | AC | 846 ms
37,764 KB |
| testcase_34 | AC | 852 ms
37,764 KB |
ソースコード
#line 1 "main.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/1919"
#line 1 "library/my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else
// https://codeforces.com/blog/entry/96344
#pragma GCC optimize("Ofast,unroll-loops")
// いまの CF だとこれ入れると動かない？
// #pragma GCC target("avx2,popcnt")
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;
template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'000'000'000;
template <>
constexpr ll infty<ll> = ll(infty<int>) * infty<int> * 2;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * infty<ll>;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;
using pi = pair<ll, ll>;
using vi = vector<ll>;
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 vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;
#define vv(type, name, h, ...) \
vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...) \
vector<vector<vector<type>>> name( \
h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...) \
vector<vector<vector<vector<type>>>> name( \
a, vector<vector<vector<type>>>( \
b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))
// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)
#define FOR_subset(t, s) \
for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if
#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second
#define stoi stoll
int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
int popcnt_mod_2(int x) { return __builtin_parity(x); }
int popcnt_mod_2(u32 x) { return __builtin_parity(x); }
int popcnt_mod_2(ll x) { return __builtin_parityll(x); }
int popcnt_mod_2(u64 x) { return __builtin_parityll(x); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
template <typename T>
T floor(T a, T b) {
return a / b - (a % b && (a ^ b) < 0);
}
template <typename T>
T ceil(T x, T y) {
return floor(x + y - 1, y);
}
template <typename T>
T bmod(T x, T y) {
return x - y * floor(x, y);
}
template <typename T>
pair<T, T> divmod(T x, T y) {
T q = floor(x, y);
return {q, x - q * y};
}
template <typename T, typename U>
T SUM(const vector<U> &A) {
T sm = 0;
for (auto &&a: A) sm += a;
return sm;
}
#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#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 UNIQUE(x) \
sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()
template <typename T>
T POP(deque<T> &que) {
T a = que.front();
que.pop_front();
return a;
}
template <typename T>
T POP(pq<T> &que) {
T a = que.top();
que.pop();
return a;
}
template <typename T>
T POP(pqg<T> &que) {
T a = que.top();
que.pop();
return a;
}
template <typename T>
T POP(vc<T> &que) {
T a = que.back();
que.pop_back();
return a;
}
template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
if (check_ok) assert(check(ok));
while (abs(ok - ng) > 1) {
auto x = (ng + ok) / 2;
(check(x) ? ok : ng) = x;
}
return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
FOR(iter) {
double x = (ok + ng) / 2;
(check(x) ? ok : ng) = x;
}
return (ok + ng) / 2;
}
template <class T, class S>
inline bool chmax(T &a, const S &b) {
return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
return (a > b ? a = b, 1 : 0);
}
// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
vc<int> A(S.size());
FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
return A;
}
template <typename T, typename U>
vector<T> cumsum(vector<U> &A, int off = 1) {
int N = A.size();
vector<T> B(N + 1);
FOR(i, N) { B[i + 1] = B[i] + A[i]; }
if (off == 0) B.erase(B.begin());
return B;
}
// stable sort
template <typename T>
vector<int> argsort(const vector<T> &A) {
vector<int> ids(len(A));
iota(all(ids), 0);
sort(all(ids),
[&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
return ids;
}
// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
vc<T> B(len(I));
FOR(i, len(I)) B[i] = A[I[i]];
return B;
}
#endif
#line 1 "library/other/io.hpp"
#define FASTIO
#include <unistd.h>
// https://judge.yosupo.jp/submission/21623
namespace fastio {
static constexpr uint32_t SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];
// pointer of ibuf, obuf
uint32_t pil = 0, pir = 0, por = 0;
struct Pre {
char num[10000][4];
constexpr Pre() : num() {
for (int i = 0; i < 10000; i++) {
int n = i;
for (int j = 3; j >= 0; j--) {
num[i][j] = n % 10 | '0';
n /= 10;
}
}
}
} constexpr pre;
inline void load() {
memcpy(ibuf, ibuf + pil, pir - pil);
pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
pil = 0;
if (pir < SZ) ibuf[pir++] = '\n';
}
inline void flush() {
fwrite(obuf, 1, por, stdout);
por = 0;
}
void rd(char &c) {
do {
if (pil + 1 > pir) load();
c = ibuf[pil++];
} while (isspace(c));
}
void rd(string &x) {
x.clear();
char c;
do {
if (pil + 1 > pir) load();
c = ibuf[pil++];
} while (isspace(c));
do {
x += c;
if (pil == pir) load();
c = ibuf[pil++];
} while (!isspace(c));
}
template <typename T>
void rd_real(T &x) {
string s;
rd(s);
x = stod(s);
}
template <typename T>
void rd_integer(T &x) {
if (pil + 100 > pir) load();
char c;
do
c = ibuf[pil++];
while (c < '-');
bool minus = 0;
if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
if (c == '-') { minus = 1, c = ibuf[pil++]; }
}
x = 0;
while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; }
if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
if (minus) x = -x;
}
}
void rd(int &x) { rd_integer(x); }
void rd(ll &x) { rd_integer(x); }
void rd(i128 &x) { rd_integer(x); }
void rd(u32 &x) { rd_integer(x); }
void rd(u64 &x) { rd_integer(x); }
void rd(u128 &x) { rd_integer(x); }
void rd(double &x) { rd_real(x); }
void rd(long double &x) { rd_real(x); }
void rd(f128 &x) { rd_real(x); }
template <class T, class U>
void rd(pair<T, U> &p) {
return rd(p.first), rd(p.second);
}
template <size_t N = 0, typename T>
void rd_tuple(T &t) {
if constexpr (N < std::tuple_size<T>::value) {
auto &x = std::get<N>(t);
rd(x);
rd_tuple<N + 1>(t);
}
}
template <class... T>
void rd(tuple<T...> &tpl) {
rd_tuple(tpl);
}
template <size_t N = 0, typename T>
void rd(array<T, N> &x) {
for (auto &d: x) rd(d);
}
template <class T>
void rd(vc<T> &x) {
for (auto &d: x) rd(d);
}
void read() {}
template <class H, class... T>
void read(H &h, T &... t) {
rd(h), read(t...);
}
void wt(const char c) {
if (por == SZ) flush();
obuf[por++] = c;
}
void wt(const string s) {
for (char c: s) wt(c);
}
void wt(const char *s) {
size_t len = strlen(s);
for (size_t i = 0; i < len; i++) wt(s[i]);
}
template <typename T>
void wt_integer(T x) {
if (por > SZ - 100) flush();
if (x < 0) { obuf[por++] = '-', x = -x; }
int outi;
for (outi = 96; x >= 10000; outi -= 4) {
memcpy(out + outi, pre.num[x % 10000], 4);
x /= 10000;
}
if (x >= 1000) {
memcpy(obuf + por, pre.num[x], 4);
por += 4;
} else if (x >= 100) {
memcpy(obuf + por, pre.num[x] + 1, 3);
por += 3;
} else if (x >= 10) {
int q = (x * 103) >> 10;
obuf[por] = q | '0';
obuf[por + 1] = (x - q * 10) | '0';
por += 2;
} else
obuf[por++] = x | '0';
memcpy(obuf + por, out + outi + 4, 96 - outi);
por += 96 - outi;
}
template <typename T>
void wt_real(T x) {
ostringstream oss;
oss << fixed << setprecision(15) << double(x);
string s = oss.str();
wt(s);
}
void wt(int x) { wt_integer(x); }
void wt(ll x) { wt_integer(x); }
void wt(i128 x) { wt_integer(x); }
void wt(u32 x) { wt_integer(x); }
void wt(u64 x) { wt_integer(x); }
void wt(u128 x) { wt_integer(x); }
void wt(double x) { wt_real(x); }
void wt(long double x) { wt_real(x); }
void wt(f128 x) { wt_real(x); }
template <class T, class U>
void wt(const pair<T, U> val) {
wt(val.first);
wt(' ');
wt(val.second);
}
template <size_t N = 0, typename T>
void wt_tuple(const T t) {
if constexpr (N < std::tuple_size<T>::value) {
if constexpr (N > 0) { wt(' '); }
const auto x = std::get<N>(t);
wt(x);
wt_tuple<N + 1>(t);
}
}
template <class... T>
void wt(tuple<T...> tpl) {
wt_tuple(tpl);
}
template <class T, size_t S>
void wt(const array<T, S> val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) wt(' ');
wt(val[i]);
}
}
template <class T>
void wt(const vector<T> val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) wt(' ');
wt(val[i]);
}
}
void print() { wt('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
wt(head);
if (sizeof...(Tail)) wt(' ');
print(forward<Tail>(tail)...);
}
// gcc expansion. called automaticall after main.
void __attribute__((destructor)) _d() { flush(); }
} // namespace fastio
using fastio::read;
using fastio::print;
using fastio::flush;
#if defined(LOCAL)
#define SHOW(...) \
SHOW_IMPL(__VA_ARGS__, SHOW4, SHOW3, SHOW2, SHOW1)(__VA_ARGS__)
#define SHOW_IMPL(_1, _2, _3, _4, NAME, ...) NAME
#define SHOW1(x) print(#x, "=", (x)), flush()
#define SHOW2(x, y) print(#x, "=", (x), #y, "=", (y)), flush()
#define SHOW3(x, y, z) print(#x, "=", (x), #y, "=", (y), #z, "=", (z)), flush()
#define SHOW4(x, y, z, w) \
print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w)), flush()
#else
#define SHOW(...)
#endif
#define INT(...) \
int __VA_ARGS__; \
read(__VA_ARGS__)
#define LL(...) \
ll __VA_ARGS__; \
read(__VA_ARGS__)
#define U32(...) \
u32 __VA_ARGS__; \
read(__VA_ARGS__)
#define U64(...) \
u64 __VA_ARGS__; \
read(__VA_ARGS__)
#define STR(...) \
string __VA_ARGS__; \
read(__VA_ARGS__)
#define CHAR(...) \
char __VA_ARGS__; \
read(__VA_ARGS__)
#define DBL(...) \
double __VA_ARGS__; \
read(__VA_ARGS__)
#define VEC(type, name, size) \
vector<type> name(size); \
read(name)
#define VV(type, name, h, w) \
vector<vector<type>> name(h, vector<type>(w)); \
read(name)
void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
#line 2 "library/mod/modint_common.hpp"
struct has_mod_impl {
template <class T>
static auto check(T &&x) -> decltype(x.get_mod(), std::true_type{});
template <class T>
static auto check(...) -> std::false_type;
};
template <class T>
class has_mod : public decltype(has_mod_impl::check<T>(std::declval<T>())) {};
template <typename mint>
mint inv(int n) {
static const int mod = mint::get_mod();
static vector<mint> dat = {0, 1};
assert(0 <= n);
if (n >= mod) n %= mod;
while (len(dat) <= n) {
int k = len(dat);
int q = (mod + k - 1) / k;
dat.eb(dat[k * q - mod] * mint::raw(q));
}
return dat[n];
}
template <typename mint>
mint fact(int n) {
static const int mod = mint::get_mod();
assert(0 <= n && n < mod);
static vector<mint> dat = {1, 1};
while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * mint::raw(len(dat)));
return dat[n];
}
template <typename mint>
mint fact_inv(int n) {
static vector<mint> dat = {1, 1};
if (n < 0) return mint(0);
while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * inv<mint>(len(dat)));
return dat[n];
}
template <class mint, class... Ts>
mint fact_invs(Ts... xs) {
return (mint(1) * ... * fact_inv<mint>(xs));
}
template <typename mint, class Head, class... Tail>
mint multinomial(Head &&head, Tail &&... tail) {
return fact<mint>(head) * fact_invs<mint>(std::forward<Tail>(tail)...);
}
template <typename mint>
mint C_dense(int n, int k) {
static vvc<mint> C;
static int H = 0, W = 0;
auto calc = [&](int i, int j) -> mint {
if (i == 0) return (j == 0 ? mint(1) : mint(0));
return C[i - 1][j] + (j ? C[i - 1][j - 1] : 0);
};
if (W <= k) {
FOR(i, H) {
C[i].resize(k + 1);
FOR(j, W, k + 1) { C[i][j] = calc(i, j); }
}
W = k + 1;
}
if (H <= n) {
C.resize(n + 1);
FOR(i, H, n + 1) {
C[i].resize(W);
FOR(j, W) { C[i][j] = calc(i, j); }
}
H = n + 1;
}
return C[n][k];
}
template <typename mint, bool large = false, bool dense = false>
mint C(ll n, ll k) {
assert(n >= 0);
if (k < 0 || n < k) return 0;
if constexpr (dense) return C_dense<mint>(n, k);
if constexpr (!large) return multinomial<mint>(n, k, n - k);
k = min(k, n - k);
mint x(1);
FOR(i, k) x *= mint(n - i);
return x * fact_inv<mint>(k);
}
template <typename mint, bool large = false>
mint C_inv(ll n, ll k) {
assert(n >= 0);
assert(0 <= k && k <= n);
if (!large) return fact_inv<mint>(n) * fact<mint>(k) * fact<mint>(n - k);
return mint(1) / C<mint, 1>(n, k);
}
// [x^d](1-x)^{-n}
template <typename mint, bool large = false, bool dense = false>
mint C_negative(ll n, ll d) {
assert(n >= 0);
if (d < 0) return mint(0);
if (n == 0) { return (d == 0 ? mint(1) : mint(0)); }
return C<mint, large, dense>(n + d - 1, d);
}
#line 3 "library/mod/modint.hpp"
template <int mod>
struct modint {
static constexpr u32 umod = u32(mod);
static_assert(umod < u32(1) << 31);
u32 val;
static modint raw(u32 v) {
modint x;
x.val = v;
return x;
}
constexpr modint() : val(0) {}
constexpr modint(u32 x) : val(x % umod) {}
constexpr modint(u64 x) : val(x % umod) {}
constexpr modint(u128 x) : val(x % umod) {}
constexpr modint(int x) : val((x %= mod) < 0 ? x + mod : x){};
constexpr modint(ll x) : val((x %= mod) < 0 ? x + mod : x){};
constexpr modint(i128 x) : val((x %= mod) < 0 ? x + mod : x){};
bool operator<(const modint &other) const { return val < other.val; }
modint &operator+=(const modint &p) {
if ((val += p.val) >= umod) val -= umod;
return *this;
}
modint &operator-=(const modint &p) {
if ((val += umod - p.val) >= umod) val -= umod;
return *this;
}
modint &operator*=(const modint &p) {
val = u64(val) * p.val % umod;
return *this;
}
modint &operator/=(const modint &p) {
*this *= p.inverse();
return *this;
}
modint operator-() const { return modint::raw(val ? mod - val : u32(0)); }
modint operator+(const modint &p) const { return modint(*this) += p; }
modint operator-(const modint &p) const { return modint(*this) -= p; }
modint operator*(const modint &p) const { return modint(*this) *= p; }
modint operator/(const modint &p) const { return modint(*this) /= p; }
bool operator==(const modint &p) const { return val == p.val; }
bool operator!=(const modint &p) const { return val != p.val; }
modint inverse() const {
int a = val, b = mod, u = 1, v = 0, t;
while (b > 0) {
t = a / b;
swap(a -= t * b, b), swap(u -= t * v, v);
}
return modint(u);
}
modint pow(ll n) const {
assert(n >= 0);
modint ret(1), mul(val);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
static constexpr int get_mod() { return mod; }
// (n, r), r は 1 の 2^n 乗根
static constexpr pair<int, int> ntt_info() {
if (mod == 120586241) return {20, 74066978};
if (mod == 167772161) return {25, 17};
if (mod == 469762049) return {26, 30};
if (mod == 754974721) return {24, 362};
if (mod == 880803841) return {23, 211};
if (mod == 943718401) return {22, 663003469};
if (mod == 998244353) return {23, 31};
if (mod == 1004535809) return {21, 836905998};
if (mod == 1045430273) return {20, 363};
if (mod == 1051721729) return {20, 330};
if (mod == 1053818881) return {20, 2789};
return {-1, -1};
}
static constexpr bool can_ntt() { return ntt_info().fi != -1; }
};
#ifdef FASTIO
template <int mod>
void rd(modint<mod> &x) {
fastio::rd(x.val);
x.val %= mod;
// assert(0 <= x.val && x.val < mod);
}
template <int mod>
void wt(modint<mod> x) {
fastio::wt(x.val);
}
#endif
using modint107 = modint<1000000007>;
using modint998 = modint<998244353>;
#line 1 "library/ds/bit_vector.hpp"
struct Bit_Vector {
int n;
vc<pair<u64, u32>> dat;
Bit_Vector(int n) : n(n) { dat.assign((n + 127) >> 6, {0, 0}); }
void set(int i) { dat[i >> 6].fi |= u64(1) << (i & 63); }
void reset() { fill(all(dat), pair<u64, u32>{0, 0}); }
void build() {
FOR(i, len(dat) - 1) dat[i + 1].se = dat[i].se + popcnt(dat[i].fi);
}
// [0, k) 内の 1 の個数
int count(int k, bool f) {
auto [a, b] = dat[k >> 6];
int ret = b + popcnt(a & ((u64(1) << (k & 63)) - 1));
return (f ? ret : k - ret);
}
int count(int L, int R, bool f) { return count(R, f) - count(L, f); }
string to_string() {
string ans;
FOR(i, n) ans += '0' + (dat[i / 64].fi >> (i % 64) & 1);
return ans;
}
};
#line 1 "library/ds/index_compression.hpp"
template <typename T>
struct Index_Compression_DISTINCT_SMALL {
static_assert(is_same_v<T, int>);
int mi, ma;
vc<int> dat;
vc<int> build(vc<int> X) {
mi = 0, ma = -1;
if (!X.empty()) mi = MIN(X), ma = MAX(X);
dat.assign(ma - mi + 2, 0);
for (auto& x: X) dat[x - mi + 1]++;
FOR(i, len(dat) - 1) dat[i + 1] += dat[i];
for (auto& x: X) { x = dat[x - mi]++; }
FOR_R(i, 1, len(dat)) dat[i] = dat[i - 1];
dat[0] = 0;
return X;
}
int operator()(ll x) { return dat[clamp<ll>(x - mi, 0, ma - mi + 1)]; }
};
template <typename T>
struct Index_Compression_SAME_SMALL {
static_assert(is_same_v<T, int>);
int mi, ma;
vc<int> dat;
vc<int> build(vc<int> X) {
mi = 0, ma = -1;
if (!X.empty()) mi = MIN(X), ma = MAX(X);
dat.assign(ma - mi + 2, 0);
for (auto& x: X) dat[x - mi + 1] = 1;
FOR(i, len(dat) - 1) dat[i + 1] += dat[i];
for (auto& x: X) { x = dat[x - mi]; }
return X;
}
int operator()(ll x) { return dat[clamp<ll>(x - mi, 0, ma - mi + 1)]; }
};
template <typename T>
struct Index_Compression_SAME_LARGE {
vc<T> dat;
vc<int> build(vc<T> X) {
vc<int> I = argsort(X);
vc<int> res(len(X));
for (auto& i: I) {
if (!dat.empty() && dat.back() == X[i]) {
res[i] = len(dat) - 1;
} else {
res[i] = len(dat);
dat.eb(X[i]);
}
}
dat.shrink_to_fit();
return res;
}
int operator()(T x) { return LB(dat, x); }
};
template <typename T>
struct Index_Compression_DISTINCT_LARGE {
vc<T> dat;
vc<int> build(vc<T> X) {
vc<int> I = argsort(X);
vc<int> res(len(X));
for (auto& i: I) { res[i] = len(dat), dat.eb(X[i]); }
dat.shrink_to_fit();
return res;
}
int operator()(T x) { return LB(dat, x); }
};
template <typename T, bool SMALL>
using Index_Compression_DISTINCT =
typename std::conditional<SMALL, Index_Compression_DISTINCT_SMALL<T>,
Index_Compression_DISTINCT_LARGE<T>>::type;
template <typename T, bool SMALL>
using Index_Compression_SAME =
typename std::conditional<SMALL, Index_Compression_SAME_SMALL<T>,
Index_Compression_SAME_LARGE<T>>::type;
// SAME: [2,3,2] -> [0,1,0]
// DISTINCT: [2,2,3] -> [0,2,1]
// (x): lower_bound(X,x) をかえす
template <typename T, bool SAME, bool SMALL>
using Index_Compression =
typename std::conditional<SAME, Index_Compression_SAME<T, SMALL>,
Index_Compression_DISTINCT<T, SMALL>>::type;
#line 2 "library/alg/monoid/add.hpp"
template <typename E>
struct Monoid_Add {
using X = E;
using value_type = X;
static constexpr X op(const X &x, const X &y) noexcept { return x + y; }
static constexpr X inverse(const X &x) noexcept { return -x; }
static constexpr X power(const X &x, ll n) noexcept { return X(n) * x; }
static constexpr X unit() { return X(0); }
static constexpr bool commute = true;
};
#line 4 "library/ds/wavelet_matrix/wavelet_matrix.hpp"
// 静的メソッドinverseの存在をチェックするテンプレート
template <typename, typename = std::void_t<>>
struct has_inverse : std::false_type {};
template <typename T>
struct has_inverse<T, std::void_t<decltype(
T::inverse(std::declval<typename T::value_type>()))>>
: std::true_type {};
struct Dummy_Data_Structure {
using MX = Monoid_Add<bool>;
void build(const vc<bool>& A) {}
};
template <typename Y, bool SMALL_Y, typename SEGTREE = Dummy_Data_Structure>
struct Wavelet_Matrix {
using Mono = typename SEGTREE::MX;
using T = typename Mono::value_type;
static_assert(Mono::commute);
int n, log, K;
Index_Compression<Y, true, SMALL_Y> IDX;
vc<Y> ItoY;
vc<int> mid;
vc<Bit_Vector> bv;
vc<SEGTREE> seg;
Wavelet_Matrix() {}
Wavelet_Matrix(const vc<Y>& A) { build(A); }
Wavelet_Matrix(const vc<Y>& A, vc<T>& SUM_Data) { build(A, SUM_Data); }
template <typename F>
Wavelet_Matrix(int n, F f) {
build(n, f);
}
template <typename F>
void build(int m, F f) {
vc<Y> A(m);
vc<T> S(m);
for (int i = 0; i < m; ++i) tie(A[i], S[i]) = f(i);
build(A, S);
}
void build(const vc<Y>& A) { build(A, vc<T>(len(A), Mono::unit())); }
void build(const vc<Y>& A, vc<T> S) {
n = len(A);
vc<int> B = IDX.build(A);
K = 0;
for (auto& x: B) chmax(K, x + 1);
ItoY.resize(K);
FOR(i, n) ItoY[B[i]] = A[i];
log = 0;
while ((1 << log) < K) ++log;
mid.resize(log), bv.assign(log, Bit_Vector(n));
vc<int> B0(n), B1(n);
vc<T> S0(n), S1(n);
seg.resize(log + 1);
seg[log].build(S);
for (int d = log - 1; d >= 0; --d) {
int p0 = 0, p1 = 0;
for (int i = 0; i < n; ++i) {
bool f = (B[i] >> d & 1);
if (!f) { B0[p0] = B[i], S0[p0] = S[i], p0++; }
if (f) { bv[d].set(i), B1[p1] = B[i], S1[p1] = S[i], p1++; }
}
swap(B, B0), swap(S, S0);
move(B1.begin(), B1.begin() + p1, B.begin() + p0);
move(S1.begin(), S1.begin() + p1, S.begin() + p0);
mid[d] = p0, bv[d].build(), seg[d].build(S);
}
}
// [L,R) x [0,y)
int prefix_count(int L, int R, Y y) {
int p = IDX(y);
if (p == 0) return 0;
if (p == K) return R - L;
int cnt = 0;
for (int d = log - 1; d >= 0; --d) {
int l0 = bv[d].count(L, 0), r0 = bv[d].count(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
if (p >> d & 1) cnt += r0 - l0, L = l1, R = r1;
if (!(p >> d & 1)) L = l0, R = r0;
}
return cnt;
}
// [L,R) x [y1,y2)
int count(int L, int R, Y y1, Y y2) {
return prefix_count(L, R, y2) - prefix_count(L, R, y1);
}
// [L,R) x [0,y)
pair<int, T> prefix_count_and_prod(int L, int R, Y y) {
int p = IDX(y);
if (p == 0) return {0, Mono::unit()};
if (p == K) return {R - L, seg[log].prod(L, R)};
int cnt = 0;
T t = Mono::unit();
for (int d = log - 1; d >= 0; --d) {
int l0 = bv[d].count(L, 0), r0 = bv[d].count(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
if (p >> d & 1) {
cnt += r0 - l0, t = Mono::op(t, seg[d].prod(l0, r0)), L = l1, R = r1;
}
if (!(p >> d & 1)) L = l0, R = r0;
}
return {cnt, t};
}
// [L,R) x [y1,y2)
pair<int, T> count_and_prod(int L, int R, Y y1, Y y2) {
if constexpr (has_inverse<Mono>::value) {
auto [c1, t1] = prefix_count_and_prod(L, R, y1);
auto [c2, t2] = prefix_count_and_prod(L, R, y2);
return {c2 - c1, Mono::op(Mono::inverse(t1), t2)};
}
int lo = IDX(y1), hi = IDX(y2), cnt = 0;
T t = Mono::unit();
auto dfs = [&](auto& dfs, int d, int L, int R, int a, int b) -> void {
assert(b - a == (1 << d));
if (hi <= a || b <= lo) return;
if (lo <= a && b <= hi) {
cnt += R - L, t = Mono::op(t, seg[d].prod(L, R));
return;
}
--d;
int c = (a + b) / 2;
int l0 = bv[d].count(L, 0), r0 = bv[d].count(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
dfs(dfs, d, l0, r0, a, c), dfs(dfs, d, l1, r1, c, b);
};
dfs(dfs, log, L, R, 0, 1 << log);
return {cnt, t};
}
// [L,R) x [y1,y2)
T prefix_prod(int L, int R, Y y) { return prefix_count_and_prod(L, R, y).se; }
// [L,R) x [y1,y2)
T prod(int L, int R, Y y1, Y y2) { return count_and_prod(L, R, y1, y2).se; }
T prod_all(int L, int R) { return seg[log].prod(L, R); }
Y kth(int L, int R, int k) {
assert(0 <= k && k < R - L);
int p = 0;
for (int d = log - 1; d >= 0; --d) {
int l0 = bv[d].count(L, 0), r0 = bv[d].count(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
if (k < r0 - l0) {
L = l0, R = r0;
} else {
k -= r0 - l0, L = l1, R = r1, p |= 1 << d;
}
}
return ItoY[p];
}
// y 以上最小 OR infty<Y>
Y next(int L, int R, Y y) {
int k = IDX(y);
int p = K;
auto dfs = [&](auto& dfs, int d, int L, int R, int a, int b) -> void {
if (p <= a || L == R || b <= k) return;
if (d == 0) {
chmin(p, a);
return;
}
--d;
int c = (a + b) / 2;
int l0 = bv[d].count(L, 0), r0 = bv[d].count(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
dfs(dfs, d, l0, r0, a, c), dfs(dfs, d, l1, r1, c, b);
};
dfs(dfs, log, L, R, 0, 1 << log);
return (p == K ? infty<Y> : ItoY[p]);
}
// y 以下最大 OR -infty<T>
Y prev(int L, int R, Y y) {
int k = IDX(y + 1);
int p = -1;
auto dfs = [&](auto& dfs, int d, int L, int R, int a, int b) -> void {
if (b - 1 <= p || L == R || k <= a) return;
if (d == 0) {
chmax(p, a);
return;
}
--d;
int c = (a + b) / 2;
int l0 = bv[d].count(L, 0), r0 = bv[d].count(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
dfs(dfs, d, l1, r1, c, b), dfs(dfs, d, l0, r0, a, c);
};
dfs(dfs, log, L, R, 0, 1 << log);
return (p == -1 ? -infty<Y> : ItoY[p]);
}
Y median(bool UPPER, int L, int R) {
assert(0 <= L && L < R && R <= n);
int k = (UPPER ? (R - L) / 2 : (R - L - 1) / 2);
return kth(L, R, k);
}
pair<Y, T> kth_value_and_prod(int L, int R, int k) {
assert(0 <= k && k <= R - L);
if (k == R - L) return {infty<Y>, seg[log].prod(L, R)};
int p = 0;
T t = Mono::unit();
for (int d = log - 1; d >= 0; --d) {
int l0 = bv[d].count(L, 0), r0 = bv[d].count(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
if (k < r0 - l0) {
L = l0, R = r0;
} else {
t = Mono::op(t, seg[d].prod(l0, r0)), k -= r0 - l0, L = l1, R = r1,
p |= 1 << d;
}
}
t = Mono::op(t, seg[0].prod(L, L + k));
return {ItoY[p], t};
}
T prod_index_range(int L, int R, int k1, int k2) {
static_assert(has_inverse<Mono>::value);
T t1 = kth_value_and_prod(L, R, k1).se;
T t2 = kth_value_and_prod(L, R, k2).se;
return Mono::op(Mono::inverse(t1), t2);
}
// [L,R) x [0,y) での check(cnt, prod) が true となる最大の (cnt,prod)
template <typename F>
pair<int, T> max_right(F check, int L, int R) {
int cnt = 0;
T t = Mono::unit();
assert(check(0, Mono::unit()));
if (check(R - L, seg[log].prod(L, R))) {
return {R - L, seg[log].prod(L, R)};
}
for (int d = log - 1; d >= 0; --d) {
int l0 = bv[d].count(L, 0), r0 = bv[d].count(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
int cnt1 = cnt + r0 - l0;
T t1 = Mono::op(t, seg[d].prod(l0, r0));
if (check(cnt1, t1)) {
cnt = cnt1, t = t1, L = l1, R = r1;
} else {
L = l0, R = r0;
}
}
return {cnt, t};
}
void set(int i, T t) {
assert(0 <= i && i < n);
int L = i, R = i + 1;
seg[log].set(L, t);
for (int d = log - 1; d >= 0; --d) {
int l0 = bv[d].count(L, 0), r0 = bv[d].count(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
if (l0 < r0) L = l0, R = r0;
if (l0 == r0) L = l1, R = r1;
seg[d].set(L, t);
}
}
void multiply(int i, T t) {
assert(0 <= i && i < n);
int L = i, R = i + 1;
seg[log].multiply(L, t);
for (int d = log - 1; d >= 0; --d) {
int l0 = bv[d].count(L, 0), r0 = bv[d].count(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
if (l0 < r0) L = l0, R = r0;
if (l0 == r0) L = l1, R = r1;
seg[d].multiply(L, t);
}
}
};
/*
// 座圧するかどうかを COMPRESS で指定する
// xor 的な使い方をする場合には、コンストラクタで log を渡すこと
template <typename T, bool COMPRESS, bool USE_SUM>
struct Wavelet_Matrix_Old {
static_assert(is_same_v<T, int> || is_same_v<T, ll>);
int N, lg;
vector<int> mid;
vector<Bit_Vector> bv;
vc<T> key;
bool set_log;
vvc<T> cumsum;
Wavelet_Matrix_Old() {}
// 和を使わないなら、SUM_data は空でよい
Wavelet_Matrix_Old(vc<T> A, vc<T> SUM_data = {}, int log = -1) {
build(A, SUM_data, log);
}
void build(vc<T> A, vc<T> SUM_data = {}, int log = -1) {
if constexpr (USE_SUM) { assert(len(SUM_data) == len(A)); }
N = len(A), lg = log, set_log = (log != -1);
if (N == 0) {
lg = 0;
cumsum.resize(1);
cumsum[0] = {0};
return;
}
vc<T>& S = SUM_data;
if (COMPRESS) {
assert(!set_log);
key.reserve(N);
vc<int> I = argsort(A);
for (auto&& i: I) {
if (key.empty() || key.back() != A[i]) key.eb(A[i]);
A[i] = len(key) - 1;
}
key.shrink_to_fit();
}
if (lg == -1) lg = __lg(max<ll>(MAX(A), 1)) + 1;
mid.resize(lg), bv.assign(lg, Bit_Vector(N));
if constexpr (USE_SUM) cumsum.assign(1 + lg, vc<T>(N + 1, 0));
S.resize(N);
vc<T> A0(N), A1(N);
vc<T> S0(N), S1(N);
FOR_R(d, -1, lg) {
int p0 = 0, p1 = 0;
if constexpr (USE_SUM) {
FOR(i, N) { cumsum[d + 1][i + 1] = cumsum[d + 1][i] + S[i]; }
}
if (d == -1) break;
FOR(i, N) {
bool f = (A[i] >> d & 1);
if (!f) {
if constexpr (USE_SUM) S0[p0] = S[i];
A0[p0++] = A[i];
} else {
if constexpr (USE_SUM) S1[p1] = S[i];
bv[d].set(i), A1[p1++] = A[i];
}
}
mid[d] = p0;
bv[d].build();
swap(A, A0), swap(S, S0);
FOR(i, p1) A[p0 + i] = A1[i], S[p0 + i] = S1[i];
}
}
// [L,R) x [a,b), (cnt, monoid value)
pair<int, T> range_cnt_sum(int L, int R, T a, T b, T xor_val = 0) {
if (xor_val != 0) assert(set_log);
if (a == b) return {0, 0};
if (COMPRESS) a = LB(key, a), b = LB(key, b);
int cnt = 0;
T sm = 0;
auto dfs = [&](auto& dfs, int d, int L, int R, T lx, T rx) -> void {
if (rx <= a || b <= lx) return;
if (a <= lx && rx <= b) {
cnt += R - L, sm += get(d, L, R);
return;
}
--d;
T mx = (lx + rx) / 2;
int l0 = bv[d].count(L, 0), r0 = bv[d].count(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
if (xor_val >> d & 1) swap(l0, l1), swap(r0, r1);
dfs(dfs, d, l0, r0, lx, mx), dfs(dfs, d, l1, r1, mx, rx);
};
dfs(dfs, lg, L, R, 0, T(1) << lg);
return {cnt, sm};
}
// smallest k, sum of [0,k)
pair<T, T> kth_value_sum(int L, int R, int k, T xor_val = 0) {
assert(0 <= k && k <= R - L);
if (k == R - L) { return {infty<T>, sum_all(L, R)}; }
if (L == R) return {infty<T>, 0};
if (xor_val != 0) assert(set_log);
T sm = 0, val = 0;
for (int d = lg - 1; d >= 0; --d) {
// いま幅 d+1 の trie node に居て, 幅 d のところに行く
int l0 = bv[d].count(L, 0), r0 = bv[d].count(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
if (xor_val >> d & 1) swap(l0, l1), swap(r0, r1);
if (k < r0 - l0) {
L = l0, R = r0;
} else {
k -= r0 - l0, val |= T(1) << d, L = l1, R = r1;
if constexpr (USE_SUM) sm += get(d, l0, r0);
}
}
if constexpr (USE_SUM) sm += get(0, L, L + k);
if (COMPRESS) val = key[val];
return {val, sm};
}
int count(int L, int R, T a, T b, T xor_val = 0) {
return range_cnt_sum(L, R, a, b, xor_val).fi;
}
T sum(int L, int R, T a, T b, T xor_val = 0) {
static_assert(USE_SUM);
return range_cnt_sum(L, R, a, b, xor_val).se;
}
T sum_index_range(int L, int R, int k1, int k2, T xor_val = 0) {
static_assert(USE_SUM);
return kth_value_sum(L, R, k2, xor_val).se
- kth_value_sum(L, R, k1, xor_val).se;
}
T kth(int L, int R, int k, T xor_val = 0) {
assert(0 <= k && k < R - L);
return kth_value_sum(L, R, k, xor_val).fi;
}
// x 以上最小 OR infty<T>
T next(int L, int R, T x, T xor_val = 0) {
if (xor_val != 0) assert(set_log);
if (L == R) return infty<T>;
if (COMPRESS) x = LB(key, x);
T ans = infty<T>;
auto dfs = [&](auto& dfs, int d, int L, int R, T lx, T rx) -> void {
if (ans <= lx || L == R || rx <= x) return;
if (d == 0) {
chmin(ans, lx);
return;
}
--d;
T mx = (lx + rx) / 2;
int l0 = bv[d].count(L, 0), r0 = bv[d].count(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
if (xor_val >> d & 1) swap(l0, l1), swap(r0, r1);
dfs(dfs, d, l0, r0, lx, mx), dfs(dfs, d, l1, r1, mx, rx);
};
dfs(dfs, lg, L, R, 0, T(1) << lg);
if (COMPRESS && ans < infty<T>) ans = key[ans];
return ans;
}
// x 以下最大 OR -infty<T>
T prev(int L, int R, T x, T xor_val = 0) {
if (xor_val != 0) assert(set_log);
if (L == R) return -infty<T>;
T ans = -infty<int>;
++x;
if (COMPRESS) x = LB(key, x);
auto dfs = [&](auto& dfs, int d, int L, int R, T lx, T rx) -> void {
if ((rx - 1) <= ans || L == R || x <= lx) return;
if (d == 0) {
chmax(ans, lx);
return;
}
--d;
T mx = (lx + rx) / 2;
int l0 = bv[d].count(L, 0), r0 = bv[d].count(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
if (xor_val >> d & 1) swap(l0, l1), swap(r0, r1);
dfs(dfs, d, l1, r1, mx, rx), dfs(dfs, d, l0, r0, lx, mx);
};
dfs(dfs, lg, L, R, 0, T(1) << lg);
if (COMPRESS && ans != -infty<T>) ans = key[ans];
return ans;
}
// xor した結果で、[L, R) の中で中央値。
// LOWER = true：下側中央値、false：上側中央値
T median(bool UPPER, int L, int R, T xor_val = 0) {
int n = R - L;
int k = (UPPER ? n / 2 : (n - 1) / 2);
return kth(L, R, k, xor_val);
}
T sum_all(int L, int R) { return get(lg, L, R); }
// check(cnt, prefix sum) が true となるような最大の (cnt, sum)
template <typename F>
pair<int, T> max_right(F check, int L, int R, T xor_val = 0) {
assert(check(0, 0));
if (xor_val != 0) assert(set_log);
if (L == R) return {0, 0};
if (check(R - L, get(lg, L, R))) return {R - L, get(lg, L, R)};
int cnt = 0;
T sm = 0;
for (int d = lg - 1; d >= 0; --d) {
int l0 = bv[d].count(L, 0), r0 = bv[d].count(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
if (xor_val >> d & 1) swap(l0, l1), swap(r0, r1);
if (check(cnt + r0 - l0, sm + get(d, l0, r0))) {
cnt += r0 - l0, sm += get(d, l0, r0);
L = l1, R = r1;
} else {
L = l0, R = r0;
}
}
int k = binary_search(
[&](int k) -> bool { return check(cnt + k, sm + get(0, L, L + k)); }, 0,
R - L);
cnt += k, sm += get(0, L, L + k);
return {cnt, sm};
}
private:
inline T get(int d, int L, int R) {
if constexpr (USE_SUM) return cumsum[d][R] - cumsum[d][L];
return 0;
}
};
*/
#line 2 "library/ds/wavelet_matrix/wavelet_matrix_2d_range.hpp"
template <typename SEGTREE, typename XY, bool SMALL_X, bool SMALL_Y>
struct Wavelet_Matrix_2D_Range {
// 点群を X 昇順に並べる.
Wavelet_Matrix<XY, SMALL_Y, SEGTREE> WM;
using Mono = typename SEGTREE::MX;
using T = typename Mono::value_type;
static_assert(Mono::commute);
Index_Compression<XY, false, SMALL_X> IDX_X;
int n;
vc<int> new_idx;
template <typename F>
Wavelet_Matrix_2D_Range(int n, F f) {
build(n, f);
}
template <typename F>
void build(int m, F f) {
n = m;
vc<XY> X(n), Y(n);
vc<T> S(n);
FOR(i, n) tie(X[i], Y[i], S[i]) = f(i);
new_idx = IDX_X.build(X);
vc<int> I(n);
FOR(i, n) I[new_idx[i]] = i;
Y = rearrange(Y, I);
S = rearrange(S, I);
WM.build(Y, S);
}
int count(XY x1, XY x2, XY y1, XY y2) {
return WM.count(IDX_X(x1), IDX_X(x2), y1, y2);
}
// [L,R) x [-inf,y)
pair<int, T> prefix_count_and_prod(XY x1, XY x2, XY y) {
return WM.prefix_count_and_prod(IDX_X(x1), IDX_X(x2), y);
}
// [L,R) x [y1,y2)
pair<int, T> count_and_prod(XY x1, XY x2, XY y1, XY y2) {
return WM.count_and_prod(IDX_X(x1), IDX_X(x2), y1, y2);
}
// [L,R) x [-inf,inf)
T prod_all(XY x1, XY x2) { return WM.prod_all(IDX_X(x1), IDX_X(x2)); }
// [L,R) x [-inf,y)
T prefix_prod(XY x1, XY x2, XY y) {
return WM.prefix_prod(IDX_X(x1), IDX_X(x2), y);
}
// [L,R) x [y1,y2)
T prod(XY x1, XY x2, XY y1, XY y2) {
return WM.prod(IDX_X(x1), IDX_X(x2), y1, y2);
}
// [L,R) x [-inf,y) での check(cnt, prod) が true となる最大の (cnt,prod)
template <typename F>
pair<int, T> max_right(F check, XY x1, XY x2) {
return WM.max_right(check, IDX_X(x1), IDX_X(x2));
}
// i は最初に渡したインデックス
void set(int i, T t) { WM.set(new_idx[i], t); }
// i は最初に渡したインデックス
void multiply(int i, T t) { WM.multiply(new_idx[i], t); }
};
#line 2 "library/alg/monoid/add_pair.hpp"
template <typename E>
struct Monoid_Add_Pair {
using value_type = pair<E, E>;
using X = value_type;
static constexpr X op(const X &x, const X &y) {
return {x.fi + y.fi, x.se + y.se};
}
static constexpr X inverse(const X &x) { return {-x.fi, -x.se}; }
static constexpr X unit() { return {0, 0}; }
static constexpr bool commute = true;
};
#line 3 "library/ds/fenwicktree/fenwicktree.hpp"
template <typename Monoid>
struct FenwickTree {
using G = Monoid;
using MX = Monoid;
using E = typename G::value_type;
int n;
vector<E> dat;
E total;
FenwickTree() {}
FenwickTree(int n) { build(n); }
template <typename F>
FenwickTree(int n, F f) {
build(n, f);
}
FenwickTree(const vc<E>& v) { build(v); }
void build(int m) {
n = m;
dat.assign(m, G::unit());
total = G::unit();
}
void build(const vc<E>& v) {
build(len(v), [&](int i) -> E { return v[i]; });
}
template <typename F>
void build(int m, F f) {
n = m;
dat.clear();
dat.reserve(n);
total = G::unit();
FOR(i, n) { dat.eb(f(i)); }
for (int i = 1; i <= n; ++i) {
int j = i + (i & -i);
if (j <= n) dat[j - 1] = G::op(dat[i - 1], dat[j - 1]);
}
total = prefix_sum(m);
}
E prod_all() { return total; }
E sum_all() { return total; }
E sum(int k) { return prefix_sum(k); }
E prod(int k) { return prefix_prod(k); }
E prefix_sum(int k) { return prefix_prod(k); }
E prefix_prod(int k) {
chmin(k, n);
E ret = G::unit();
for (; k > 0; k -= k & -k) ret = G::op(ret, dat[k - 1]);
return ret;
}
E sum(int L, int R) { return prod(L, R); }
E prod(int L, int R) {
chmax(L, 0), chmin(R, n);
if (L == 0) return prefix_prod(R);
assert(0 <= L && L <= R && R <= n);
E pos = G::unit(), neg = G::unit();
while (L < R) { pos = G::op(pos, dat[R - 1]), R -= R & -R; }
while (R < L) { neg = G::op(neg, dat[L - 1]), L -= L & -L; }
return G::op(pos, G::inverse(neg));
}
vc<E> get_all() {
vc<E> res(n);
FOR(i, n) res[i] = prod(i, i + 1);
return res;
}
void add(int k, E x) { multiply(k, x); }
void multiply(int k, E x) {
static_assert(G::commute);
total = G::op(total, x);
for (++k; k <= n; k += k & -k) dat[k - 1] = G::op(dat[k - 1], x);
}
template <class F>
int max_right(const F check, int L = 0) {
assert(check(G::unit()));
E s = G::unit();
int i = L;
// 2^k 進むとダメ
int k = [&]() {
while (1) {
if (i % 2 == 1) { s = G::op(s, G::inverse(dat[i - 1])), i -= 1; }
if (i == 0) { return topbit(n) + 1; }
int k = lowbit(i) - 1;
if (i + (1 << k) > n) return k;
E t = G::op(s, dat[i + (1 << k) - 1]);
if (!check(t)) { return k; }
s = G::op(s, G::inverse(dat[i - 1])), i -= i & -i;
}
}();
while (k) {
--k;
if (i + (1 << k) - 1 < len(dat)) {
E t = G::op(s, dat[i + (1 << k) - 1]);
if (check(t)) { i += (1 << k), s = t; }
}
}
return i;
}
// check(i, x)
template <class F>
int max_right_with_index(const F check, int L = 0) {
assert(check(L, G::unit()));
E s = G::unit();
int i = L;
// 2^k 進むとダメ
int k = [&]() {
while (1) {
if (i % 2 == 1) { s = G::op(s, G::inverse(dat[i - 1])), i -= 1; }
if (i == 0) { return topbit(n) + 1; }
int k = lowbit(i) - 1;
if (i + (1 << k) > n) return k;
E t = G::op(s, dat[i + (1 << k) - 1]);
if (!check(i + (1 << k), t)) { return k; }
s = G::op(s, G::inverse(dat[i - 1])), i -= i & -i;
}
}();
while (k) {
--k;
if (i + (1 << k) - 1 < len(dat)) {
E t = G::op(s, dat[i + (1 << k) - 1]);
if (check(i + (1 << k), t)) { i += (1 << k), s = t; }
}
}
return i;
}
template <class F>
int min_left(const F check, int R) {
assert(check(G::unit()));
E s = G::unit();
int i = R;
// false になるところまで戻る
int k = 0;
while (i > 0 && check(s)) {
s = G::op(s, dat[i - 1]);
k = lowbit(i);
i -= i & -i;
}
if (check(s)) {
assert(i == 0);
return 0;
}
// 2^k 進むと ok になる
// false を維持して進む
while (k) {
--k;
E t = G::op(s, G::inverse(dat[i + (1 << k) - 1]));
if (!check(t)) { i += (1 << k), s = t; }
}
return i + 1;
}
int kth(E k, int L = 0) {
return max_right([&k](E x) -> bool { return x <= k; }, L);
}
};
#line 8 "main.cpp"
using mint = modint107;
void solve() {
LL(N);
VEC(int, A, N);
VEC(int, B, N);
pair<mint, mint> ANS;
FOR(2) {
swap(ANS.fi, ANS.se);
swap(A, B);
auto I = argsort(A);
A = rearrange(A, I);
B = rearrange(B, I);
vc<int> X(N), Y(N);
FOR(i, N) X[i] = A[i] - B[i];
FOR(i, N) Y[i] = A[i] + B[i];
using Grp = Monoid_Add_Pair<mint>;
Wavelet_Matrix_2D_Range<FenwickTree<Grp>, int, false, false> WM(
N, [&](int i) -> tuple<int, int, pair<mint, mint>> {
return {X[i], Y[i], Grp::unit()};
});
FOR(i, N) {
WM.multiply(i, {mint(1), mint(A[i])});
auto [c, s] = WM.prod(-infty<int>, X[i], -infty<int>, Y[i]);
ANS.fi += mint(A[i]) * c - s;
}
}
ANS.fi *= mint(2);
ANS.se *= mint(2);
print(ANS);
}
signed main() {
solve();
return 0;
}