結果
| 問題 | No.148 試験監督（3） |
| コンテスト | |
| ユーザー |
 zeta
|
| 提出日時 | 2026-02-23 07:20:35 |
| 言語 | C++23 (gcc 15.2.0 + boost 1.89.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 61,852 bytes |
| 記録 | |
| コンパイル時間 | 10,018 ms |
| コンパイル使用メモリ | 389,944 KB |
| 実行使用メモリ | 31,000 KB |
| 最終ジャッジ日時 | 2026-02-23 11:42:02 |
| 合計ジャッジ時間 | 23,372 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge2 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | TLE * 12 |
ソースコード
#line 1 "No_148_\u8a66\u9a13\u76e3\u7763_3.cpp"
#define YRSD
#line 1 "YRS/aa/fast.hpp"
#include <bits/allocator.h>
#pragma GCC optimize("Ofast,unroll-loops")
#pragma GCC target("avx2,popcnt")
#line 2 "YRS/all.hpp"
#line 2 "YRS/aa/head.hpp"
#include <iostream>
#include <algorithm>
#include <array>
#include <bitset>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <string>
#include <tuple>
#include <bit>
#include <chrono>
#include <functional>
#include <iomanip>
#include <utility>
#include <type_traits>
#include <cassert>
#include <cctype>
#include <cmath>
#include <cstring>
#include <ctime>
#include <limits>
#include <ranges>
#include <concepts>
#define TE template <typename T>
#define TES template <typename T, typename ...S>
#define Z auto
#define ep emplace_back
#define eb emplace
#define fi first
#define se second
#define all(x) (x).begin(), (x).end()
#define OV4(a, b, c, d, e, ...) e
#define FOR1(a) for (int _ = 0; _ < (a); ++_)
#define FOR2(i, a) for (int i = 0; i < (a); ++i)
#define FOR3(i, a, b) for (int i = (a); i < (b); ++i)
#define FOR4(i, a, b, c) for (int i = (a); i < (b); i += (c))
#define FOR(...) OV4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR1_R(a) for (int _ = (a) - 1; _ >= 0; --_)
#define FOR2_R(i, a) for (int i = (a) - 1; i >= 0; --i)
#define FOR3_R(i, a, b) for (int i = (b) - 1; i >= (a); --i)
#define FOR4_R(i, a, b, c) for (int i = (b) - 1; i >= (a); i -= (c))
#define FOR_R(...) OV4(__VA_ARGS__, FOR4_R, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)
#define FOR_subset(t, s) for (int t = (s); t > -1; t = (t == 0 ? -1 : (t - 1) & s))
#define sort ranges::sort
using namespace std;
TE using vc = vector<T>;
TE using vvc = vc<vc<T>>;
TE using T1 = tuple<T>;
TE using T2 = tuple<T, T>;
TE using T3 = tuple<T, T, T>;
TE using T4 = tuple<T, T, T, T>;
TE using max_heap = priority_queue<T>;
TE using min_heap = priority_queue<T, vc<T>, greater<T>>;
using u8 = unsigned char; using uint = unsigned int; using ll = long long; using ull = unsigned long long;
using ld = long double; using i128 = __int128; using u128 = __uint128_t; using f128 = __float128;
using u16 = uint16_t;
using PII = pair<int, int>; using PLL = pair<ll, ll>;
#ifdef YRSD
constexpr bool dbg = 1;
#else
constexpr bool dbg = 0;
#endif
#line 2 "YRS/IO/IO.hpp"
istream &operator>>(istream &I, i128 &x) {
static string s;
I >> s;
int f = s[0] == '-';
x = 0;
const int N = (int)s.size();
FOR(i, f, N) x = x * 10 + s[i] - '0';
if (f) x = -x;
return I;
}
ostream &operator<<(ostream &O, i128 x) {
static string s;
s.clear();
bool f = x < 0;
if (f) x = -x;
while (x) s += '0' + x % 10, x /= 10;
if (s.empty()) s += '0';
if (f) s += '-';
reverse(all(s));
return O << s;
}
istream &operator>>(istream &I, f128 &x) {
static string s;
I >> s, x = stold(s);
return I;
}
ostream &operator<<(ostream &O, const f128 x) { return O << ld(x); }
template <typename... S>
istream &operator>>(istream &I, tuple<S...> &t) {
return apply([&I](Z &...s) { ((I >> s), ...); }, t), I;
}
template <typename T, typename U>
istream &operator>>(istream &I, pair<T, U> &x) {
return I >> x.fi >> x.se;
}
template <typename T, typename U>
ostream &operator<<(ostream &O, const pair<T, U> &x) {
return O << x.fi << ' ' << x.se;
}
TE requires requires(T &c) { begin(c); end(c); } and
(not is_same_v<decay_t<T>, string>)
istream &operator>>(istream &I, T &c) {
for (Z &e : c) I >> e;
return I;
}
TE requires requires(const T &c) { begin(c); end(c); } and
(not is_same_v<decay_t<T>, const char*>) and
(not is_same_v<decay_t<T>, string>) and
(not is_array_v<remove_reference_t<T>> or
not is_same_v<remove_extent_t<remove_reference_t<T>>, char>)
ostream &operator<<(ostream &O, const T &a) {
if (a.empty()) return O;
Z i = a.begin();
O << *i++;
for (; i != a.end(); ++i) O << ' ' << *i;
return O;
}
void IN() {}
TE void IN(T &x, Z &...s) { cin >> x, IN(s...); }
void print() { cout << '\n'; }
TES void print(T &&x, S &&...y) {
cout << x;
if constexpr (sizeof...(S)) cout << ' ';
print(forward<S>(y)...);
}
void put() { cout << ' '; }
TES void put(T &&x, S &&...y) {
cout << x;
if constexpr (sizeof...(S)) cout << ' ';
put(forward<S>(y)...);
}
#define INT(...) int __VA_ARGS__; IN(__VA_ARGS__)
#define UINT(...) uint __VA_ARGS__; IN(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__; IN(__VA_ARGS__)
#define ULL(...) ull __VA_ARGS__; IN(__VA_ARGS__)
#define I128(...) i128 __VA_ARGS__; IN(__VA_ARGS__)
#define STR(...) string __VA_ARGS__; IN(__VA_ARGS__)
#define CH(...) char __VA_ARGS__; IN(__VA_ARGS__)
#define REAL(...) re __VA_ARGS__; IN(__VA_ARGS__)
#define VEC(T, a, n) vc<T> a(n); IN(a)
void YES(bool o = 1) { print(o ? "YES" : "NO"); }
void Yes(bool o = 1) { print(o ? "Yes" : "No"); }
void yes(bool o = 1) { print(o ? "yes" : "no"); }
void NO(bool o = 1) { YES(not o); }
void No(bool o = 1) { Yes(not o); }
void no(bool o = 1) { yes(not o); }
void ALICE(bool o = 1) { print(o ? "ALICE" : "BOB"); }
void Alice(bool o = 1) { print(o ? "Alice" : "Bob"); }
void alice(bool o = 1) { print(o ? "alice" : "bob"); }
void BOB(bool o = 1) { ALICE(not o); }
void Bob(bool o = 1) { Alice(not o); }
void bob(bool o = 1) { alice(not o); }
void POSSIBLE(bool o = 1) { print(o ? "POSSIBLE" : "IMPOSSIBLE"); }
void Possible(bool o = 1) { print(o ? "Possible" : "Impossible"); }
void possible(bool o = 1) { print(o ? "possible" : "impossible"); }
void IMPOSSIBLE(bool o = 1) { POSSIBLE(not o); }
void Impossible(bool o = 1) { Possible(not o); }
void impossible(bool o = 1) { possible(not o); }
void TAK(bool o = 1) { print(o ? "TAK" : "NIE"); }
void NIE(bool o = 1) { TAK(not o); }
#line 5 "YRS/all.hpp"
#if (__cplusplus >= 202002L)
#include <numbers>
constexpr ld pi = numbers::pi;
#endif
TE constexpr T inf = numeric_limits<T>::max();
template <> constexpr i128 inf<i128> = i128(inf<ll>) * 2'000'000'000'000'000'000;
template <typename T, typename U>
constexpr pair<T, U> inf<pair<T, U>> = {inf<T>, inf<U>};
TE constexpr static inline int pc(T x) { return popcount(make_unsigned_t<T>(x)); }
constexpr static inline ll len(const Z &a) { return a.size(); }
void reverse(Z &a) { reverse(all(a)); }
void unique(Z &a) {
sort(a);
a.erase(unique(all(a)), a.end());
}
TE vc<int> inverse(const vc<T> &a) {
int N = len(a);
vc<int> b(N, -1);
FOR(i, N) if (a[i] != -1) b[a[i]] = i;
return b;
}
Z QMAX(const Z &a) { return *max_element(all(a)); }
Z QMIN(const Z &a) { return *min_element(all(a)); }
TE Z QMAX(T l, T r) { return *max_element(l, r); }
TE Z QMIN(T l, T r) { return *min_element(l, r); }
constexpr bool chmax(Z &a, const Z &b) { return (a < b ? a = b, 1 : 0); }
constexpr bool chmin(Z &a, const Z &b) { return (a > b ? a = b, 1 : 0); }
vc<int> argsort(const Z &a) {
vc<int> I(len(a));
iota(all(I), 0);
sort(I, [&](int i, int k) { return a[i] < a[k] or (a[i] == a[k] and i < k); });
return I;
}
TE vc<T> rearrange(const vc<T> &a, const vc<int> &I) {
int N = len(I);
vc<T> b(N);
FOR(i, N) b[i] = a[I[i]];
return b;
}
template <int of = 1, typename T>
vc<T> pre_sum(const vc<T> &a) {
int N = len(a);
vc<T> c(N + 1);
FOR(i, N) c[i + 1] = c[i] + a[i];
if (of == 0) c.erase(c.begin());
return c;
}
TE constexpr static int topbit(T x) {
if (x == 0) return - 1;
if constexpr (sizeof(T) <= 4) return 31 - __builtin_clz(x);
else return 63 - __builtin_clzll(x);
}
TE constexpr static int lowbit(T x) {
if (x == 0) return -1;
if constexpr (sizeof(T) <= 4) return __builtin_ctz(x);
else return __builtin_ctzll(x);
}
TE constexpr T floor(T x, T y) { return x / y - (x % y and (x ^ y) < 0); }
TE constexpr T ceil(T x, T y) { return floor(x + y - 1, y); }
TE constexpr T bmod(T x, T y) { return x - floor(x, y) * y; }
TE constexpr pair<T, T> divmod(T x, T y) {
T q = floor(x, y);
return pair{q, x - q * y};
}
template <typename T = ll>
T SUM(const Z &v) {
return accumulate(all(v), T(0));
}
int lb(const Z &a, Z x) { return lower_bound(all(a), x) - a.begin(); }
TE int lb(T l, T r, Z x) { return lower_bound(l, r, x) - l; }
int ub(const Z &a, Z x) { return upper_bound(all(a), x) - a.begin(); }
TE int ub(T l, T r, Z x) { return upper_bound(l, r, x) - l; }
template <bool ck = 1>
ll bina(Z f, ll l, ll r) {
if constexpr (ck) assert(f(l));
while (abs(l - r) > 1) {
ll x = (r + l) >> 1;
(f(x) ? l : r) = x;
}
return l;
}
TE T bina_real(Z f, T l, T r, int c = 100) {
while (c--) {
T x = (l + r) / 2;
(f(x) ? l : r) = x;
}
return (l + r) / 2;
}
Z pop(Z &s) {
if constexpr (requires { s.pop_back(); }) {
Z x = s.back();
return s.pop_back(), x;
} else if constexpr (requires { s.top(); }) {
Z x = s.top();
return s.pop(), x;
} else {
Z x = s.front();
return s.pop(), x;
}
}
void setp(int x) { cout << fixed << setprecision(x); }
TE inline void sh(vc<T> &a, int N, T b = {}) {
a.resize(N, b);
}
#line 1 "YRS/debug.hpp"
#ifdef YRSD
void DBG() { cerr << "]" << endl; }
TES void DBG(T &&x, S &&...y) {
cerr << x;
if constexpr (sizeof...(S)) cerr << ", ";
DBG(forward<S>(y)...);
}
#define debug(...) cerr << "[" << __LINE__ << "]: [" #__VA_ARGS__ "] = [", DBG(__VA_ARGS__)
void ERR() { cerr << endl; }
TES void ERR(T &&x, S &&...y) {
cerr << x;
if constexpr (sizeof...(S)) cerr << ", ";
ERR(forward<S>(y)...);
}
#define err(...) cerr << "[" << __LINE__ << "]: ", ERR(__VA_ARGS__)
#define asser assert
#else
#define debug(...) void(0721)
#define err(...) void(0721)
#define asser(...) void(0721)
#endif
#line 2 "YRS/IO/fast_io.hpp"
#define FIO
static constexpr uint SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];
// pointer of ibuf, obuf
uint 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;
}
inline void rd(char &c) {
do {
if (pil + 1 > pir) load();
c = ibuf[pil++];
} while (isspace(c));
}
inline 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));
}
TE inline void rd_real(T &x) {
string s;
rd(s);
x = stod(s);
}
TE inline 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;
}
}
inline void rd(int16_t &x) { rd_integer(x); }
inline void rd(uint16_t &x) { rd_integer(x); }
inline void rd(int &x) { rd_integer(x); }
inline void rd(long &x) { rd_integer(x); }
inline void rd(ll &x) { rd_integer(x); }
inline void rd(i128 &x) { rd_integer(x); }
inline void rd(uint &x) { rd_integer(x); }
inline void rd(ull &x) { rd_integer(x); }
inline void rd(u128 &x) { rd_integer(x); }
inline void rd(double &x) { rd_real(x); }
inline void rd(long double &x) { rd_real(x); }
inline void rd(f128 &x) { rd_real(x); }
template <typename T, typename U>
inline void rd(pair<T, U> &p) {
return rd(p.fi), rd(p.se);
}
template <size_t N = 0, typename T>
inline void rd_tuple(T &t) {
if constexpr (N < tuple_size<T>::value) {
Z &x = get<N>(t);
rd(x);
rd_tuple<N + 1>(t);
}
}
template <typename... T>
inline void rd(tuple<T...> &tpl) {
rd_tuple(tpl);
}
template <size_t N = 0, typename T>
inline void rd(array<T, N> &x) {
for (Z &e : x) rd(e);
}
TE inline void rd(vc<T> &x) {
for (Z &e : x) rd(e);
}
inline void read() {}
template <typename H, typename... T>
inline void read(H &h, T &...t) {
rd(h), read(t...);
}
inline void wt(const char c) {
if (por == SZ) flush();
obuf[por++] = c;
}
inline void wt(const string s) {
for (char c : s) wt(c);
}
inline void wt(const char *s) {
size_t len = strlen(s);
for (size_t i = 0; i < len; i++) wt(s[i]);
}
TE inline 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;
}
TE inline void wt_real(T x) {
ostringstream oss;
oss << fixed << setprecision(10) << double(x);
string s = oss.str();
wt(s);
}
inline void wt(int x) { wt_integer(x); }
inline void wt(long x) { wt_integer(x); }
inline void wt(ll x) { wt_integer(x); }
inline void wt(i128 x) { wt_integer(x); }
inline void wt(uint x) { wt_integer(x); }
inline void wt(ull x) { wt_integer(x); }
inline void wt(u128 x) { wt_integer(x); }
inline void wt(double x) { wt_real(x); }
inline void wt(long double x) { wt_real(x); }
inline void wt(f128 x) { wt_real(x); }
template <typename T, typename U>
inline void wt(const pair<T, U> &val) {
wt(val.fi);
wt(' ');
wt(val.se);
}
template <size_t N = 0, typename T>
inline void wt_tuple(const T &t) {
if constexpr (N < tuple_size<T>::value) {
if constexpr (N > 0) {
wt(' ');
}
const Z x = get<N>(t);
wt(x);
wt_tuple<N + 1>(t);
}
}
template <typename... T>
inline void wt(tuple<T...> &tpl) {
wt_tuple(tpl);
}
template <typename T, size_t S>
inline void wt(const array<T, S> &val) {
Z n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) wt(' ');
wt(val[i]);
}
}
TE inline void wt(const vc<T> &a) {
int N = len(a);
FOR(i, N) {
if (i) wt(' ');
wt(a[i]);
}
}
TE inline void wt(const vc<vc<T>> &v) {
int N = len(v);
FOR(i, N) {
wt(v[i]);
if (i + 1 != N) wt('\n');
}
}
template <typename T, const size_t s>
inline void wt(const vc<array<T, s>> &v) {
int N = len(v);
FOR(i, N) {
wt(v[i]);
if (i + 1 != N) wt('\n');
}
}
// gcc expansion. called automaticall after main.
inline void __attribute__((destructor)) _d() { flush(); }
inline void println() { wt('\n'); }
template <typename Head, typename... Tail>
inline void println(Head &&head, Tail &&...tail) {
wt(head);
if (sizeof...(Tail)) wt(' ');
println(forward<Tail>(tail)...);
}
#define IN(...) read(__VA_ARGS__)
#define print(...) println(__VA_ARGS__)
#define FLUSH() flush()
#line 6 "No_148_\u8a66\u9a13\u76e3\u7763_3.cpp"
// #include "YRS/random/rng.hpp"
// #include "YRS/ds/basic/retsu.hpp"
#line 2 "YRS/mod/mint.hpp"
#line 2 "YRS/mod/modint_common.hpp"
TE concept is_mint = requires(T x) {
{ T::get_mod() };
{ T::gen(0ull) } -> same_as<T>;
x.val;
};
TE concept has_const_mod =
requires { integral_constant<int, (int)T::get_mod()> {}; };
TE static vc<T> &invs() {
static vc<T> a{0, 1};
return a;
}
TE static vc<T> &fac() {
static vc<T> a{1, 1};
return a;
}
TE static vc<T> &ifac() {
static vc<T> a{1, 1};
return a;
}
TE static int Set_inv(int N) {
static vc<T> &inv = invs<T>();
if (len(inv) >= N) return N;
inv.resize(N + 1);
inv[0] = 1, inv[1] = 1;
FOR(i, 1, N) inv[i + 1] = inv[i] * i;
T t = pop(inv).inv();
FOR_R(i, N) inv[i] *= t, t *= i;
return N;
}
TE static int Set_comb(int N) {
static vc<T> &fa = fac<T>(), &ifa = ifac<T>();
if (len(fa) >= N) return N;
fa.resize(N);
ifa.resize(N);
FOR(i, 1, N) fa[i] = fa[i - 1] * i;
ifa[N - 1] = fa[N - 1].inv();
FOR_R(i, N - 1) ifa[i] = ifa[i + 1] * (i + 1);
return N;
}
template <typename mint>
mint inv(int n) {
static const int mod = mint::get_mod();
static vc<mint> &a = invs<mint>();
assert(0 <= n);
while (len(a) <= n) {
int k = len(a);
int q = (mod + k - 1) / k;
int r = k * q - mod;
a.ep(a[r] * mint(q));
}
return a[n];
}
template <typename mint>
mint fact(int n) {
static const int mod = mint::get_mod();
static vc<mint> &a = fac<mint>();
assert(0 <= n);
if (n >= mod) return 0;
while (len(a) <= n) {
int k = len(a);
a.ep(a[k - 1] * mint(k));
}
return a[n];
}
template <typename mint>
mint fact_inv(int n) {
static vc<mint> &a = ifac<mint>();
if (n < 0) return mint(0);
while (len(a) <= n)
a.ep(a[len(a) - 1] * inv<mint>(len(a)));
return a[n];
}
template <typename mint, typename... Ts>
mint fact_invs(Ts... xs) {
return (mint(1) * ... * fact_inv<mint>(xs));
}
template <typename mint, typename X, typename... S>
mint multinomial(X&& a, S&&... b) {
return fact<mint>(a) * fact_invs<mint>(forward<S>(b)...);
}
template <typename mint>
mint C_dense(int n, int k) {
assert(n >= 0);
if (k < 0 or n < k) return 0;
static vc<vc<mint>> C;
static int H = 0, W = 0;
Z 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 (int i = 0; i < H; ++i) {
C[i].resize(k + 1);
for (int j = W; j < k + 1; ++j) {
C[i][j] = calc(i, j);
}
}
W = k + 1;
}
if (H <= n) {
C.resize(n + 1);
for (int i = H; i < n + 1; ++i) {
C[i].resize(W);
for (int j = 0; j < W; ++j) {
C[i][j] = calc(i, j);
}
}
H = n + 1;
}
return C[n][k];
}
template <typename mint>
mint C(int N, int K) {
assert(N >= 0);
if (K < 0 or N < K) return 0;
return fact<mint>(N) * fact_inv<mint>(K) * fact_inv<mint>(N - K);
}
template <typename mint>
mint lucas(ll N, ll K) {
static constexpr int P = mint::get_mod();
if (K > N) return 0;
if (K == 0) return 1;
return C<mint>(N % P, K % P) * lucas<mint>(N / P, K / P);
}
template <typename mint, bool large = false, bool dense = false>
mint binom(ll n, ll k) {
assert(n >= 0);
if (k < 0 or n < k) return 0;
if constexpr (dense) return C_dense<mint>(n, k);
if constexpr (not 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 and k <= n);
if (not large) return fact_inv<mint>(n) * fact<mint>(k) * fact<mint>(n - k);
return mint(1) / binom<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 binom<mint, large, dense>(n + d - 1, d);
}
#define CC C<mint>
#define fac fact<mint>
#define ifac fact_inv<mint>
#define set_comb Set_comb<mint>
#define set_inv Set_inv<mint>
#line 4 "YRS/mod/mint.hpp"
#define C constexpr
template <int mod>
struct mint_t {
using mint = mint_t;
static C uint m = mod;
uint x;
C uint val() const { return x; }
C mint_t() : x(0) {}
C mint_t(uint x) : x(x % m) {}
C mint_t(ull x) : x(x % m) {}
C mint_t(u128 x) : x(x % m) {}
C mint_t(int x) : x((x %= mod) < 0 ? x + mod : x) {}
C mint_t(ll x) : x((x %= mod) < 0 ? x + mod : x) {}
C mint_t(i128 x) : x((x %= mod) < 0 ? x + mod : x) {}
C mint &operator+=(mint p) {
if ((x += p.x) >= m) x -= m;
return *this;
}
C mint &operator-=(mint p) {
if ((x += m - p.x) >= m) x -= m;
return *this;
}
C mint operator+(mint p) const { return mint(*this) += p; }
C mint operator-(mint p) const { return mint(*this) -= p; }
C mint &operator*=(mint p) {
x = ull(x) * p.x % m;
return *this;
}
C mint operator*(mint p) const { return mint(*this) *= p; }
C mint &operator/=(mint p) { return *this *= p.inv(); }
C mint operator/(mint p) const { return mint(*this) /= p; }
C mint operator-() const { return mint::gen(x ? mod - x : 0); }
C mint inv() const {
int a = x, b = mod, x = 1, y = 0;
while (b > 0) {
int t = a / b;
swap(a -= t * b, b);
swap(x -= t * y, y);
}
return mint(x);
}
C mint pow(ll k) const {
if (k < 0) return inv().pow(-k);
mint s(1), a(x);
for (; k; k >>= 1, a *= a)
if (k & 1) s *= a;
return s;
}
C bool operator<(mint p) const { return x < p.x; }
C bool operator==(mint p) const { return x == p.x; }
C bool operator!=(mint p) const { return x != p.x; }
static C mint gen(uint x) {
mint s;
s.x = x;
return s;
}
friend istream &operator>>(istream &cin, mint &p) {
ll t;
cin >> t;
p = t;
return cin;
}
friend ostream &operator<<(ostream &cout, mint p) { return cout << p.x; }
static C int get_mod() { return mod; }
static C PII ntt_info() {
if (mod == 167772161) return {25, 17};
if (mod == 469762049) return {26, 30};
if (mod == 754974721) return {24, 362};
if (mod == 998244353) return {23, 31};
if (mod == 120586241) return {20, 74066978};
if (mod == 880803841) return {23, 211};
if (mod == 943718401) return {22, 663003469};
if (mod == 1004535809) return {21, 582313106};
if (mod == 1012924417) return {21, 368093570};
return {-1, -1};
}
static C bool can_ntt() { return ntt_info().fi != -1; }
};
#undef C
using M99 = mint_t<998244353>;
using M17 = mint_t<1000000007>;
#ifdef FIO
template <int mod>
void rd(mint_t<mod> &x) {
LL(y);
x = y;
}
template <int mod>
void wt(mint_t<mod> x) {
wt(x.x);
}
#endif
#line 2 "YRS/po/f/factorials.hpp"
#line 2 "YRS/po/f/stiling_1.hpp"
#line 2 "YRS/po/taylor.hpp"
#line 2 "YRS/po/convolution.hpp"
#line 2 "YRS/po/c/ntt.hpp"
#line 4 "YRS/po/c/ntt.hpp"
template <typename mint>
void ntt(vc<mint> &a, bool in) {
assert(mint::can_ntt());
const int p = mint::ntt_info().fi;
const uint m = mint::get_mod();
static array<mint, 30> r, ir, ra, ira, rat, irat;
assert(p != -1 and len(a) <= (1 << max(0, p)));
static bool ok = 0;
if (not ok) {
ok = 1;
r[p] = mint::ntt_info().se;
ir[p] = mint(1) / r[p];
FOR_R(i, p) {
r[i] = r[i + 1] * r[i + 1];
ir[i] = ir[i + 1] * ir[i + 1];
}
mint s = 1, in = 1;
FOR(i, p - 1) {
ra[i] = r[i + 2] * s;
ira[i] = ir[i + 2] * in;
s *= ir[i + 2];
in *= r[i + 2];
}
s = 1, in = 1;
FOR(i, p - 2) {
rat[i] = r[i + 3] * s;
irat[i] = ir[i + 3] * in;
s *= ir[i + 3];
in *= r[i + 3];
}
}
int N = len(a), n = topbit(N);
if (not in) {
int sz = 0;
while (sz < n) {
if (n - sz == 1) {
int p = 1 << (n - sz - 1);
mint c = 1;
FOR(s, 1 << sz) {
int of = s << (n - sz);
FOR(i, p) {
mint l = a[i + of], r = a[i + of + p] * c;
a[i + of] = l + r, a[i + of + p] = l - r;
}
c *= ra[topbit(~s & -~s)];
}
++sz;
} else {
int p = 1 << (n - sz - 2);
mint c = 1, in = r[2];
FOR(s, 1 << sz) {
mint r2 = c * c, r3 = r2 * c;
int of = s << (n - sz);
FOR(i, p) {
const ull mm = ull(m) * m;
ull a0 = a[i + of].val(), a1 = ull(a[i + of + p].val()) * c.val();
ull aa = ull(a[i + of + 2 * p].val()) * r2.val();
ull bb = ull(a[i + of + 3 * p].val()) * r3.val();
ull t = (a1 + mm - bb) % m * in.val();
ull na = mm - aa;
a[i + of] = a0 + a1 + aa + bb;
a[i + of + p] = a0 + aa + mm * 2 - a1 - bb;
a[i + of + 2 * p] = a0 + na + t;
a[i + of + 3 * p] = a0 + na + mm - t;
}
c *= rat[topbit(~s & -~s)];
}
sz += 2;
}
}
} else {
mint c = mint(1) / mint(N);
FOR(i, N) a[i] *= c;
int sz = n;
while (sz) {
if (sz == 1) {
int p = 1 << (n - sz);
mint c = 1;
FOR(s, 1 << (sz - 1)) {
int of = s << (n - sz + 1);
FOR(i, p) {
ull l = a[i + of].val(), r = a[i + of + p].val();
a[i + of] = l + r;
a[i + of + p] = (m + l - r) * c.val();
}
c *= ira[topbit(~s & -~s)];
}
--sz;
} else {
int p = 1 << (n - sz);
mint c = 1, in = ir[2];
FOR(s, 1 << (sz - 2)) {
mint r2 = c * c, r3 = r2 * c;
int of = s << (n - sz + 2);
FOR(i, p) {
ull a0 = a[i + of].val(), a1 = a[i + of + p].val();
ull aa = a[i + of + 2 * p].val();
ull bb = a[i + of + 3 * p].val();
ull x = (m + aa - bb) * in.val() % m;
a[i + of] = a0 + a1 + aa + bb;
a[i + of + p] = (a0 + m - a1 + x) * c.val();
a[i + of + 2 * p] = (a0 + a1 + 2 * m - aa - bb) * r2.val();
a[i + of + 3 * p] = (a0 + 2 * m - a1 - x) * r3.val();
}
c *= irat[topbit(~s & -~s)];
}
sz -= 2;
}
}
}
}
#line 2 "YRS/mod/crt3.hpp"
constexpr uint pw_c(ull a, ull b, uint mod) {
a %= mod;
ull res = 1;
FOR(32) {
if (b & 1) res = res * a % mod;
a = a * a % mod, b >>= 1;
}
return res;
}
template <typename T, uint p0, uint p1>
T crt(ull a0, ull a1) {
static_assert(p0 < p1);
static constexpr ull x0_1 = pw_c(p0, p1 - 2, p1);
ull c = (a1 - a0 + p1) * x0_1 % p1;
return a0 + c * p0;
}
template <typename T, uint p0, uint p1, uint p2>
T crt(ull a0, ull a1, ull a2) {
static_assert(p0 < p1 and p1 < p2);
static constexpr ull x1 = pw_c(p0, p1 - 2, p1);
static constexpr ull x2 = pw_c(ull(p0) * p1 % p2, p2 - 2, p2);
static constexpr ull p01 = ull(p0) * p1;
ull c = (a1 - a0 + p1) * x1 % p1;
ull ans_1 = a0 + c * p0;
c = (a2 - ans_1 % p2 + p2) * x2 % p2;
return T(ans_1) + T(c) * T(p01);
}
template <typename T, uint p0, uint p1, uint p2, uint p3>
T crt(ull a0, ull a1, ull a2, ull a3) {
static_assert(p0 < p1 and p1 < p2 and p2 < p3);
static constexpr ull x1 = pw_c(p0, p1 - 2, p1);
static constexpr ull x2 = pw_c(ull(p0) * p1 % p2, p2 - 2, p2);
static constexpr ull x3 = pw_c(ull(p0) * p1 % p3 * p2 % p3, p3 - 2, p3);
static constexpr ull p01 = ull(p0) * p1;
ull c = (a1 - a0 + p1) * x1 % p1;
ull ans_1 = a0 + c * p0;
c = (a2 - ans_1 % p2 + p2) * x2 % p2;
u128 ans_2 = ans_1 + c * u128(p01);
c = (a3 - ans_2 % p3 + p3) * x3 % p3;
return T(ans_2) + T(c) * T(p01) * T(p2);
}
template <typename T, uint p0, uint p1, uint p2, uint p3, uint p4>
T crt(ull a0, ull a1, ull a2, ull a3, ull a4) {
static_assert(p0 < p1 and p1 < p2 and p2 < p3 and p3 < p4);
static constexpr ull x1 = pw_c(p0, p1 - 2, p1);
static constexpr ull x2 = pw_c(ull(p0) * p1 % p2, p2 - 2, p2);
static constexpr ull x3 = pw_c(ull(p0) * p1 % p3 * p2 % p3, p3 - 2, p3);
static constexpr ull x4 = pw_c(ull(p0) * p1 % p4 * p2 % p4 * p3 % p4, p4 - 2, p4);
static constexpr ull p01 = ull(p0) * p1;
static constexpr ull p23 = ull(p2) * p3;
ull c = (a1 - a0 + p1) * x1 % p1;
ull ans_1 = a0 + c * p0;
c = (a2 - ans_1 % p2 + p2) * x2 % p2;
u128 ans_2 = ans_1 + c * u128(p01);
c = ull(a3 - ans_2 % p3 + p3) * x3 % p3;
u128 ans_3 = ans_2 + u128(c * p2) * p01;
c = ull(a4 - ans_3 % p4 + p4) * x4 % p4;
return T(ans_3) + T(c) * T(p01) * T(p23);
}
#line 5 "YRS/po/convolution.hpp"
TE vc<T> conv_naive(const vc<T> &a, const vc<T> &b) {
int N = len(a), M = len(b), sz = N + M - 1;
if (not N or not M) return {};
if (N > M) return conv_naive(b, a);
vc<T> c(sz);
FOR(i, N) FOR(k, M) c[i + k] += a[i] * b[k];
return c;
}
TE vc<T> conv_ntt(vc<T> a, vc<T> b) {
assert(T::can_ntt());
if (a.empty() or b.empty()) return {};
int N = len(a), M = len(b), sz = 1;
while (sz < N + M - 1) sz <<= 1;
sh(a, sz), sh(b, sz);
bool ok = a == b;
ntt(a, 0);
if (ok) b = a;
else ntt(b, 0);
FOR(i, sz) a[i] *= b[i];
ntt(a, 1);
sh(a, N + M - 1);
return a;
}
TE vc<T> conv_mtt(const vc<T> &a, const vc<T> &b) {
int N = len(a), M = len(b);
if (not N or not M) return {};
static constexpr int p0 = 167772161;
static constexpr int p1 = 469762049;
static constexpr int p2 = 754974721;
using M0 = mint_t<p0>;
using M1 = mint_t<p1>;
using M2 = mint_t<p2>;
vc<M0> a0(N), b0(M);
vc<M1> a1(N), b1(M);
vc<M2> a2(N), b2(M);
FOR(i, N) a0[i] = a[i].val(), a1[i] = a[i].val(), a2[i] = a[i].val();
FOR(i, M) b0[i] = b[i].val(), b1[i] = b[i].val(), b2[i] = b[i].val();
vc<M0> c0 = conv_ntt<M0>(a0, b0);
vc<M1> c1 = conv_ntt<M1>(a1, b1);
vc<M2> c2 = conv_ntt<M2>(a2, b2);
vc<T> c(len(c0));
FOR(i, N + M - 1) c[i] = crt<T, p0, p1, p2>(c0[i].val(), c1[i].val(), c2[i].val());
return c;
}
TE vc<T> convolution(const vc<T> &a, const vc<T> &b) {
int N = len(a), M = len(b);
if (not N or not M) return {};
if (min(N, M) <= 30) return conv_naive(a, b);
if (T::can_ntt()) return conv_ntt(a, b);
return conv_mtt(a, b);
}
#line 2 "YRS/po/bs.hpp"
#line 2 "YRS/po/c/inte.hpp"
#line 4 "YRS/po/c/inte.hpp"
// 不定积分
template <typename mint>
vc<mint> inte(const vc<mint> &f) {
int N = len(f);
vc<mint> g(N + 1);
FOR(i, 1, N + 1) g[i] = f[i - 1] * inv<mint>(i);
return g;
}
// 定积分
template <typename mint>
mint inte(const vc<mint> &f, mint l, mint r) {
mint s = 0, L = 1, R = 1;
int N = len(f);
FOR(i, N) {
L *= l, R *= r;
s += inv<mint>(i + 1) * f[i] * (L - R);
}
return s;
}
#line 2 "YRS/po/c/diff.hpp"
#line 4 "YRS/po/c/diff.hpp"
template <typename mint>
vc<mint> diff(const vc<mint> &f) {
int N = len(f);
if (N <= 1) return {};
vc<mint> g(N - 1);
FOR(i, N - 1) g[i] = f[i + 1] * mint(i + 1);
return g;
}
#line 6 "YRS/po/bs.hpp"
template <typename mint>
vc<mint> &operator+=(vc<mint> &a, const vc<mint> &b) {
int N = len(b);
if (N > len(a)) sh(a, N);
FOR(i, N) a[i] += b[i];
return a;
}
template <typename mint>
vc<mint> operator+(const vc<mint> &a, const vc<mint> &b) {
vc<mint> c(a);
return c += b;
}
template <typename mint>
vc<mint> &operator-=(vc<mint> &a, const vc<mint> &b) {
int N = len(b);
if (N > len(a)) sh(a, N);
FOR(i, N) a[i] -= b[i];
return a;
}
template <typename mint>
vc<mint> operator-(const vc<mint> &a, const vc<mint> &b) {
vc<mint> c(a);
return c -= b;
}
template <typename mint>
vc<mint> operator*(const vc<mint> &a, const vc<mint> &b) {
return convolution(a, b);
}
#define D_poly() vc<mint> operator"" _p(ull x) { return vc<mint>{x}; } vc<mint> operator"" _p(const char *s, size_t le) {vc<mint> res;int sgn = 1, op = 0, coef = 0, ch = 0, sz = le;ll x = 0;Z re = [&](int i) {if (len(res) <= i) res.resize(i + 1);};Z cl = [&]() {if (op == -1) re(1), res[1] += sgn * coef;else if (op == 0) re(0), res[0] += sgn * (int)x;else if (op == 1) re(x), res[x] += sgn * coef;else assert(0);op = 0, x = 0, ch = 0;};FOR(i, sz) {if (s[i] == '+') cl(), sgn = 1;else if (s[i] == '-') cl(), sgn = -1;else if (isdigit(s[i])) {assert(op == 0 or op == 1);if (op == 0) ch = 1, x = (x * 10ll + s[i] - 48) % mint::get_mod();else x = x * 10ll + s[i] - 48, assert(x < 1e8);} else if (s[i] == 'x') {assert(s[i + 1] == '^' or s[i + 1] == '+' or s[i + 1] == '-' or s[i + 1] == 0);op = -1;coef = ch ? x : 1;x = 0;} else if (s[i] == '^') {assert(op == -1);op = 1;}}cl();return res; }
#line 2 "YRS/mod/powertable.hpp"
#line 2 "YRS/pr/ptable.hpp"
// [0, lm]
inline vc<int> ptable(int lm) {
++lm;
static constexpr int sz = 32768;
static int N = 2;
static vc<int> s{2}, vis(sz + 1);
if (N < lm) {
N = lm;
s = {2}, vis.assign(sz + 1, 0);
int R = lm / 2;
s.reserve(int(lm / log(lm) * 1.1));
vc<PII> cp;
FOR(i, 3, sz + 1, 2) {
if (not vis[i]) {
cp.ep(i, 1ll * i * i / 2);
FOR(j, 1ll * i * i, sz + 1, i << 1) vis[j] = 1;
}
}
FOR(L, 1, R + 1, sz) {
array<bool, sz> f{};
for (Z &[p, id] : cp)
for (int i = id; i < sz + L; id = (i += p)) f[i - L] = 1;
FOR(i, min(sz, R - L)) if (not f[i]) s.ep((L + i) << 1 | 1);
}
}
int k = lb(s, lm + 1);
return {s.begin(), s.begin() + k};
}
#line 4 "YRS/mod/powertable.hpp"
// https://codeforces.com/contest/1194/problem/F
// x^0, ..., x^N
template <typename mint>
vc<mint> power_table_1(mint x, int N) {
vc<mint> f(N + 1, 1);
FOR(i, N) f[i + 1] = f[i] * x;
return f;
}
// 0^x, ..., N^x
template <typename mint>
vc<mint> power_table_2(ll x, ll N) {
vc<mint> f(N + 1, 1);
f[0] = mint(0).pow(x);
for (int p : ptable(N)) {
if (p > N) break;
mint xp = mint(p).pow(x);
ll pp = p;
while (pp < N + 1) {
ll i = pp;
while (i < N + 1) f[i] *= xp, i += pp;
pp *= p;
}
}
return f;
}
#line 5 "YRS/po/taylor.hpp"
// f(x) -> f(x + c) 左移
template <typename mint>
vc<mint> taylor(vc<mint> f, mint c) {
if (c == mint(0)) return f;
int N = len(f);
FOR(i, N) f[i] *= fact<mint>(i);
vc<mint> b = power_table_1(c, N);
FOR(i, N) b[i] *= fact_inv<mint>(i);
reverse(all(f));
f = convolution(f, b);
f.resize(N);
reverse(all(f));
FOR(i, N) f[i] *= fact_inv<mint>(i);
return f;
}
#line 2 "YRS/po/fps_pow.hpp"
#line 2 "YRS/po/fps_exp.hpp"
#line 2 "YRS/po/c/count_terms.hpp"
// 非 0 数量
template<typename mint>
int count_terms(const vc<mint> &f){
int s = 0, N = len(f);
FOR(i, N) if(f[i] != mint(0)) ++s;
return s;
}
#line 7 "YRS/po/fps_exp.hpp"
template <typename mint>
vc<mint> fps_exp_sparse(const vc<mint> &f) {
int N = len(f);
if (N == 0) return {mint(1)};
assert(f[0] == 0);
vc<pair<int, mint>> dat;
FOR(i, 1, N) if (f[i] != mint(0)) dat.ep(i - 1, f[i] * mint(i));
vc<mint> F(N);
F[0] = 1;
FOR(i, 1, N) {
mint s = 0;
for (Z [x, y] : dat) {
if (x > i - 1) break;
s += y * F[i - 1 - x];
}
F[i] = s * inv<mint>(i);
}
return F;
}
template <typename mint>
vc<mint> fps_exp_ntt(const vc<mint> &f) {
int N = len(f);
assert(N > 0 and f[0] == mint(0));
vc<mint> s{1, (1 < N ? f[1] : 0)}, c{1}, a, b{1, 1};
while (len(s) < N) {
int m = len(s);
Z y = s;
sh(y, m << 1);
ntt(y, 0);
a = b;
vc<mint> z(m);
FOR(i, m) z[i] = y[i] * a[i];
ntt(z, 1);
FOR(i, m >> 1) z[i] = 0;
ntt(z, 0);
FOR(i, m) z[i] *= -a[i];
ntt(z, 1);
// FOR(i, m >> 1, m) c.ep(z[i]);
c.insert(c.end(), z.begin() + m / 2, z.end());
b = c;
sh(b, m << 1);
ntt(b, 0);
vc<mint> x(f.begin(), f.begin() + m);
FOR(i, m - 1) x[i] = x[i + 1] * mint(i + 1);
x.back() = 0;
ntt(x, 0);
FOR(i, m) x[i] *= y[i];
ntt(x, 1);
FOR(i, m - 1) x[i] -= s[i + 1] * mint(i + 1);
sh(x, m << 1);
FOR(i, m - 1) x[m + i] = x[i], x[i] = 0;
ntt(x, 0);
FOR(i, m << 1) x[i] *= b[i];
ntt(x, 1);
FOR_R(i, len(x) - 1) x[i + 1] = x[i] * inv<mint>(i + 1);
x[0] = 0;
FOR(i, m, min(N, m << 1)) x[i] += f[i];
FOR(i, m) x[i] = 0;
ntt(x, 0);
FOR(i, m << 1) x[i] *= y[i];
ntt(x, 1);
s.insert(s.end(), x.begin() + m, x.end());
}
sh(s, N);
return s;
}
template <typename mint>
vc<mint> fps_exp_dense(const vc<mint> &e) {
if constexpr (mint::can_ntt()) return fps_exp_ntt(e);
vc<mint> h = e;
int N = len(h);
assert(N > 0 and h[0] == mint(0));
int log = 0;
while (1 << log < N) ++log;
h.resize(1 << log);
Z dh = diff(h);
vc<mint> f = {1}, g = {1};
int m = 1;
vc<mint> p;
FOR(log) {
p = f * g;
sh(p, m);
p = p * g;
sh(p, m);
sh(g, m);
FOR(i, m) g[i] += g[i] - p[i];
p = {dh.begin(), dh.begin() + m - 1};
p = f * p;
sh(p, m + m - 1);
FOR(i, m + m - 1) p[i] = -p[i];
FOR(i, m - 1) p[i] += mint(i + 1) * f[i + 1];
p = p * g;
sh(p, m + m - 1);
FOR(i, m - 1) p[i] += dh[i];
p = inte(p);
FOR(i, m + m) p[i] = h[i] - p[i];
p[0] += mint(1);
f = f * p;
sh(f, m << 1);
m <<= 1;
}
sh(f, N);
return f;
}
template <typename mint>
vc<mint> fps_exp(const vc<mint> &f) {
int n = count_terms(f), t = mint::can_ntt() ? 320 : 3000;
return n <= t ? fps_exp_sparse(f) : fps_exp_dense(f);
}
#line 2 "YRS/po/fps_log.hpp"
#line 2 "YRS/po/fps_div.hpp"
#line 2 "YRS/po/fps_inv.hpp"
#line 5 "YRS/po/fps_inv.hpp"
// O(NK)
template <typename mint>
vc<mint> fps_inv_sparse(const vc<mint> &f) {
int N = len(f);
vc<pair<int, mint>> dat;
FOR(i, 1, N) if (f[i] != mint(0)) dat.ep(i, f[i]);
vc<mint> g(N);
mint t = mint(1) / f[0];
g[0] = t;
FOR(i, 1, N) {
mint s = 0;
for (Z &&[x, y] : dat) {
if (x > i) break;
s -= y * g[i - x];
}
g[i] = s * t;
}
return g;
}
template <typename mint>
vc<mint> fps_inv_dense_ntt(const vc<mint> &a) {
vc<mint> s{mint(1) / a[0]};
int N = len(a), n = 1;
s.reserve(N);
for (; n < N; n <<= 1) {
vc<mint> f(n << 1), g(n << 1);
int L = min(N, n << 1);
FOR(i, L) f[i] = a[i];
FOR(i, n) g[i] = s[i];
ntt(f, 0);
ntt(g, 0);
FOR(i, n << 1) f[i] *= g[i];
ntt(f, 1);
FOR(i, n) f[i] = 0;
ntt(f, 0);
FOR(i, n << 1) f[i] *= g[i];
ntt(f, 1);
FOR(i, n, L) s.ep(-f[i]);
}
return s;
}
template <typename mint>
vc<mint> fps_inv_dense(const vc<mint> &a) {
if constexpr (mint::can_ntt()) return fps_inv_dense_ntt(a);
int N = len(a), n = 1;
vc<mint> R{mint(1) / a[0]}, p;
while (n < N) {
p = convolution(R, R);
p.resize(n << 1);
vc<mint> f = {a.begin(), a.begin() + min(n << 1, N)};
p = convolution(p, f);
R.resize(n << 1);
FOR(i, n << 1) R[i] = R[i] + R[i] - p[i];
n <<= 1;
}
R.resize(N);
return R;
}
template <typename mint>
vc<mint> fps_inv(const vc<mint> &f) {
assert(f[0] != mint(0));
int sz = count_terms(f), c = mint::can_ntt() ? 160 : 820;
return sz <= c ? fps_inv_sparse(f) : fps_inv_dense(f);
}
#line 5 "YRS/po/fps_div.hpp"
template <typename mint>
vc<mint> fps_div_sprase(vc<mint> f, vc<mint> g) {
if (g[0] != mint(1)) {
mint c = g[0].inv();
for (Z &x : f) x *= c;
for (Z &x : g) x *= c;
}
vc<pair<int, mint>> dat;
int N = len(g);
FOR(i, 1, N) if (g[i] != mint(0)) dat.ep(i, -g[i]);
N = len(f);
FOR(i, N) for (Z [x, y] : dat) if (i >= x) f[i] += y * f[i - x];
return f;
}
template <typename mint>
vc<mint> fps_div_dense_ntt(const vc<mint> &f, const vc<mint> &g) {
int N = len(f), M = len(g);
if (N == 1) return {f[0] / g[0]};
int m = 1;
while (m + m < N) m <<= 1;
vc<mint> gs(g), a(m << 1), b(m << 1);
sh(gs, m);
gs = fps_inv(gs);
sh(gs, m << 1);
ntt(gs, 0);
FOR(i, m) a[i] = f[i];
FOR(i, m, N) a[i] = 0;
ntt(a, 0);
FOR(i, m << 1) a[i] *= gs[i];
ntt(a, 1);
vc<mint> s(N);
FOR(i, m) s[i] = a[i];
FOR(i, m, m << 1) a[i] = 0;
ntt(a, 0);
FOR(i, min(m << 1, M)) b[i] = g[i];
FOR(i, min(m << 1, M), m << 1) b[i] = 0;
ntt(b, 0);
FOR(i, m << 1) a[i] *= b[i];
ntt(a, 1);
FOR(i, m) a[i] = 0;
FOR(i, m, min(m << 1, N)) a[i] -= f[i];
ntt(a, 0);
FOR(i, m << 1) a[i] *= gs[i];
ntt(a, 1);
FOR(i, m, N) s[i] -= a[i];
return s;
}
// f/g 截断的商
template <typename mint>
vc<mint> fps_div_dense(vc<mint> f, vc<mint> g) {
int N = len(f);
g.resize(N);
g = fps_inv(g);
f = convolution(f, g);
f.resize(N);
return f;
}
template <typename mint>
vc<mint> fps_div(const vc<mint> &f, const vc<mint> &g) {
if (count_terms(f) < 100) return fps_div_sprase(f, g);
if constexpr (mint::can_ntt()) return fps_div_dense_ntt(f, g);
return fps_div_dense(f, g);
}
#line 5 "YRS/po/fps_log.hpp"
template <typename mint>
vc<mint> fps_log_sparse(const vc<mint> &a) {
int N = len(a);
vc<pair<int, mint>> dat;
FOR(i, 1, N) if (a[i] != mint(0)) dat.ep(i, a[i]);
vc<mint> f(N), g(N - 1);
FOR(i, N - 1) {
mint s = a[i + 1] * mint(i + 1);
for (Z &&[x, y] : dat) {
if (x > i) break;
s -= y * g[i - x];
}
g[i] = s;
f[i + 1] = s * inv<mint>(i + 1);
}
return f;
}
template <typename mint>
vc<mint> fps_log_dense(const vc<mint> &f) {
assert(f[0] == mint(1));
int N = len(f);
vc<mint> fs(f);
FOR(i, N) fs[i] *= i;
fs = fps_div_dense_ntt(fs, f);
FOR(i, N) fs[i] *= inv<mint>(i);
return fs;
}
template <typename mint>
vc<mint> fps_log(const vc<mint> &f) {
assert(f[0] == mint(1));
int n = count_terms(f), t = mint::can_ntt() ? 200 : 1200;
return n <= t ? fps_log_sparse(f) : fps_log_dense(f);
}
#line 5 "YRS/po/fps_pow.hpp"
template <typename mint>
vc<mint> fps_pw_sparse(const vc<mint> &f, mint k) {
int N = len(f);
assert(N == 0 or f[0] == mint(1));
vc<pair<int, mint>> dat;
FOR(i, 1, N) if (f[i] != mint(0)) dat.ep(i, f[i]);
vc<mint> g(N);
g[0] = 1;
FOR(i, N - 1) {
mint &s = g[i + 1];
for (Z &&[x, y] : dat) {
if (x > i + 1) break;
mint t = y * g[i - x + 1];
s += t * (k * mint(x) - mint(i - x + 1));
}
s *= inv<mint>(i + 1);
}
return g;
}
template <typename mint>
vc<mint> fps_pw_dense(const vc<mint> &f, mint k) {
assert(f[0] == mint(1));
Z g = fps_log(f);
int N = len(f);
FOR(i, N) g[i] *= k;
return fps_exp_dense(g);
}
template <typename mint>
vc<mint> fps_pw(const vc<mint> &f, mint k) {
int n = count_terms(f), t = mint::can_ntt() ? 100 : 1300;
return n <= t ? fps_pw_sparse(f, k) : fps_pw_dense(f, k);
}
template <typename mint>
vc<mint> fps_pow(const vc<mint> &f, ll k) {
assert(0 <= k);
int N = len(f);
if (k == 0) {
vc<mint> g(N);
g[0] = 1;
return g;
}
if (f[0] == mint(1)) return fps_pw(f, mint(k));
int d = N;
FOR_R(i, N) if (f[i] != mint(0)) d = i;
if (d >= ceil<ll>(N, k)) return vc<mint>(N);
int of = d * k;
mint c = f[d], in = mint(1) / c;
vc<mint> g(N - of);
FOR(i, N - of) g[i] = f[d + i] * in;
g = fps_pw(g, mint(k));
vc<mint> r(N);
c = c.pow(k);
N = len(g);
FOR(i, N) r[of + i] = g[i] * c;
return r;
}
#line 2 "YRS/ds/basic/retsu.hpp"
TE struct retsu {
int N, M;
vc<T> a;
retsu(int N, int M, T bs = T()) : N(N), M(M), a(N * M, bs) {}
T* operator[](int i) { return a.data() + i * M; }
const T* operator[](int i) const { return a.data() + i * M; }
void fill(T x) { std::fill(all(a), x); }
T max() const { return QMAX(a); }
T min() const { return QMIN(a); }
vc<vc<T>> to_vector() const {
vector res(N, vc<T>(M));
FOR(i, N) FOR(k, M) res[i][k] = a[i * M + k];
return res;
}
};
TE istream &operator>>(istream &I, retsu<T> &a) {
for (Z &e : a.a) I >> e;
return I;
}
TE ostream &operator<<(ostream &O, retsu<T> &a) {
FOR(i, a.N) FOR(k, a.M) O << a[i][k] << " \n"[k + 1 == a.M and i + 1 != a.N];
return O;
}
#ifdef FIO
TE inline void rd(retsu<T> &a) {
for (T &x : a.a) rd(x);
}
TE inline void wt(retsu<T> &a) {
FOR(i, a.N) {
FOR(k, a.M) {
if (k) wt(' ');
wt(a[i][k]);
}
if (i != a.M) wt('\n');
}
}
#endif
#line 7 "YRS/po/f/stiling_1.hpp"
// n个不同元素构成k个环的数量
// 无符号：上升阶乘 x(x+1)...(x+n-1) c(n, k)
// 有符号：下降阶乘 x(x-1)...(x-n+1) s(n, k) = (-1)^(n-k) c(n, k)
template <typename mint>
retsu<mint> stiling_1_mat(int N, int K, bool sgn = 0) {
retsu<mint> f(N + 1, K + 1);
f[0][0] = 1;
FOR(i, 1, N + 1) FOR(k, i + 1) {
if (k > K) break;
mint &x = f[i][k];
if (k) x += f[i - 1][k - 1];
x -= f[i - 1][k] * mint(i - 1);
}
if (not sgn) {
FOR(n, N + 1) FOR(i, n + 1) {
if (i > K) break;
if ((n + i) & 1) f[n][i] = -f[n][i];
}
}
return f;
}
template <typename mint>
vc<mint> stiling_1_dit(int N) {
if (N == 0) return {1};
if (N == 1) return {0, 1};
Z f = stiling_1_dit<mint>(N >> 1), g = taylor(f, -mint(N >> 1));
f = f * g;
if (N & 1) f = f * vc<mint>{mint(1 - N), 1};
return f;
}
// 固定 n ，[0, N] 的 c(n, k) s(n, k)
template <typename mint>
vc<mint> stiling_1_n(int N, bool sgn = 0) {
Z f = stiling_1_dit<mint>(N);
if (not sgn) FOR(i, N + 1) if ((N + i) & 1) f[i] = -f[i];
return f;
}
// 固定 k ，[0, N] 的 c(n, k) s(n, k)
template <typename mint>
vc<mint> stiling_1_k(int N, int K, bool sgn = 0) {
if (N < K) return vc<mint>(N + 1);
int d = N - K + 1;
vc<mint> f(d);
FOR(i, d) f[i] = inv<mint>(i + 1);
f = fps_pow(f, K);
if (sgn) FOR(i, d) if (i & 1) f[i] = -f[i];
mint c = ifac(K);
vc<mint> g(N + 1);
FOR(i, d) g[K + i] = c * f[i] * fac(K + i);
return g;
}
// s(n, i) for [N - K, N]
template <typename mint>
vc<mint> stiling_1_suf(ll N, ll K) {
vc<mint> a(K + 1), b(K + 1);
mint c = 1;
FOR(i, K + 1) {
c *= N;
a[i] = ifac(i + 1) * c;
b[i] = ifac(i + 1);
}
vc<mint> s = fps_div(a, b);
FOR(i, K + 1) s[i] *= fac(i);
vc<mint> f(K + 1);
FOR(i, 1, K + 1) f[i] = s[i] * inv<mint>(i) * (2 * (i & 1) - 1);
f = fps_exp(f);
reverse(f);
return f;
}
#line 2 "YRS/po/multipoint.hpp"
#line 2 "YRS/mod/all_inv.hpp"
template <typename mint>
vc<mint> all_inv(vc<mint> &a) {
int N = len(a);
vc<mint> c(N + 1);
c[0] = mint(1);
FOR(i, N) c[i + 1] = c[i] * a[i];
mint t = pop(c).inv();
FOR_R(i, N) c[i] *= t, t *= a[i];
return c;
}
#line 2 "YRS/po/mid_prod.hpp"
#line 4 "YRS/po/mid_prod.hpp"
// n, m 次多項式 (n>=m) a, b → n-m 次多項式 c
// c[i] = sum_j b[j]a[i+j]
// a * ~b [M - 1, N - 1]
template <typename mint>
vc<mint> mid_prod(const vc<mint> &a, const vc<mint> &b) {
int N = len(a), M = len(b);
if (b.empty()) return vc<mint>(N + 1);
if (min(M, N - M + 1) <= 60) {
vc<mint> c(N - M + 1);
FOR(i, N - M + 1) FOR(k, M) c[i] += b[k] * a[i + k];
return c;
}
if constexpr (mint::can_ntt()) {
int n = 1 << topbit(2 * N - 1);
vc<mint> fa(n), fb(n);
copy(all(a), fa.begin());
copy(b.rbegin(), b.rend(), fb.begin());
ntt(fa, 0), ntt(fb, 0);
FOR(i, n) fa[i] *= fb[i];
ntt(fa, 1);
fa.resize(N);
fa.erase(fa.begin(), fa.begin() + M - 1);
return fa;
} else {
vc<mint> fa(b.rbegin(), b.rend());
Z f = a * fa;
f.resize(N);
f.erase(f.begin(), f.begin() + M - 1);
return f;
}
}
#line 2 "YRS/po/c/ntt_db.hpp"
#line 2 "YRS/po/c/transposed_ntt.hpp"
template <typename mint>
void transposed_ntt(vc<mint> &a, bool in) {
static_assert(mint::can_ntt());
constexpr int p = mint::ntt_info().fi;
constexpr uint mod = mint::get_mod();
static array<mint, 30> r, ir, rt, irt, rat, irat;
assert(p != -1 and len(a) <= (1 << max(0, p)));
static bool ok = 0;
if (not ok) {
ok = 1;
r[p] = mint::ntt_info().se;
ir[p] = mint(1) / r[p];
FOR_R(i, p) {
r[i] = r[i + 1] * r[i + 1];
ir[i] = ir[i + 1] * ir[i + 1];
}
mint s = 1, in = 1;
FOR(i, p - 1) {
rt[i] = r[i + 2] * s;
irt[i] = ir[i + 2] * in;
s *= ir[i + 2];
in *= r[i + 2];
}
s = 1, in = 1;
FOR(i, p - 2) {
rat[i] = r[i + 3] * s;
irat[i] = ir[i + 3] * in;
s *= ir[i + 3];
in *= r[i + 3];
}
}
int N = len(a), n = topbit(N);
assert(N == 1 << n);
if (not in) {
int sz = n;
while (sz > 0) {
if (sz == 1) {
int p = 1 << (n - sz);
mint c = 1;
FOR(s, 1 << (sz - 1)) {
int of = s << (n - sz + 1);
FOR(i, p) {
ull l = a[i + of].val, r = a[i + of + p].val;
a[i + of] = l + r, a[i + of + p] = (mod + l - r) * c.val;
}
c *= rt[topbit(~s & -~s)];
}
--sz;
} else {
int p = 1 << (n - sz);
mint c = 1, in = r[2];
FOR(s, 1 << (sz - 2)) {
int of = s << (n - sz + 2);
mint r2 = c * c, r3 = r2 * c;
FOR(i, p) {
ull a0 = a[i + of + 0 * p].val;
ull a1 = a[i + of + 1 * p].val;
ull a2 = a[i + of + 2 * p].val;
ull a3 = a[i + of + 3 * p].val;
ull x = (mod + a2 - a3) * in.val % mod;
a[i + of] = a0 + a1 + a2 + a3;
a[i + of + 1 * p] = (a0 + mod - a1 + x) * c.val;
a[i + of + 2 * p] = (a0 + a1 + 2 * mod - a2 - a3) * r2.val;
a[i + of + 3 * p] = (a0 + 2 * mod - a1 - x) * r3.val;
}
c *= rat[topbit(~s & -~s)];
}
sz -= 2;
}
}
} else {
mint c = mint(1) / mint(len(a));
FOR(i, len(a)) a[i] *= c;
int sz = 0;
while (sz < n) {
if (sz == n - 1) {
int p = 1 << (n - sz - 1);
mint c = 1;
FOR(s, 1 << sz) {
int of = s << (n - sz);
FOR(i, p) {
mint l = a[i + of], r = a[i + of + p] * c;
a[i + of] = l + r, a[i + of + p] = l - r;
}
c *= irt[topbit(~s & -~s)];
}
++sz;
} else {
int p = 1 << (n - sz - 2);
mint c = 1, in = ir[2];
FOR(s, 1 << sz) {
mint r2 = c * c, r3 = r2 * c;
int of = s << (n - sz);
FOR(i, p) {
ull m2 = ull(mod) * mod;
ull a0 = a[i + of].val;
ull a1 = ull(a[i + of + p].val) * c.val;
ull a2 = ull(a[i + of + 2 * p].val) * r2.val;
ull a3 = ull(a[i + of + 3 * p].val) * r3.val;
ull t = (a1 + m2 - a3) % mod * in.val;
ull na = m2 - a2;
a[i + of] = a0 + a1 + a2 + a3;
a[i + of + 1 * p] = a0 + a2 + (2 * m2 - a1 - a3);
a[i + of + 2 * p] = a0 + na + t;
a[i + of + 3 * p] = a0 + na + m2 - t;
}
c *= irat[topbit(~s & -~s)];
}
sz += 2;
}
}
}
}
#line 5 "YRS/po/c/ntt_db.hpp"
template <typename mint, bool transposed = false>
void ntt_db(vc<mint> &a) {
static array<mint, 30> rt;
static bool ok = 0;
if (not ok) {
ok = 1;
constexpr int s = mint::ntt_info().fi;
rt[s] = mint::ntt_info().se;
FOR_R(i, s) rt[i] = rt[i + 1] * rt[i + 1];
}
if constexpr (not transposed) {
int N = len(a);
Z b = a;
ntt(b, 1);
mint r = 1, z = rt[topbit(N << 1)];
FOR(i, N) b[i] *= r, r *= z;
ntt(b, 0);
copy(all(b), std::back_inserter(a));
} else {
int N = len(a) >> 1;
vc<mint> t{a.begin(), a.begin() + N};
a = {a.begin() + N, a.end()};
transposed_ntt(a, 0);
mint r = 1, z = rt[topbit(N << 1)];
FOR(i, N) a[i] *= r, r *= z;
transposed_ntt(a, 1);
FOR(i, N) a[i] += t[i];
}
}
#line 8 "YRS/po/multipoint.hpp"
template <typename mint>
struct subprod_tree {
int m, sz;
vc<vc<mint>> v;
subprod_tree(const vc<mint> &f) {
m = len(f);
sz = 1;
while (sz < m) sz <<= 1;
v.resize(sz << 1);
FOR(i, sz) v[i + sz] = {1, (i < m ? -f[i] : 0)};
FOR_R(i, 1, sz) v[i] = convolution(v[i << 1], v[i << 1 | 1]);
}
vc<mint> eval(vc<mint> f) {
int n = len(f);
if (n == 0) return vc<mint>(m, mint(0));
f.resize(2 * n - 1);
vc<vc<mint>> g(sz << 1);
g[1] = v[1];
g[1].resize(n);
g[1] = fps_inv(g[1]);
g[1] = mid_prod(f, g[1]);
g[1].resize(sz);
FOR(i, 1, sz) {
g[i << 1] = mid_prod(g[i], v[i << 1 | 1]);
g[i << 1 | 1] = mid_prod(g[i], v[i << 1]);
}
vc<mint> c(m);
FOR(i, m) c[i] = g[sz + i][0];
return c;
}
vc<mint> inte(const vc<mint> &f) {
assert(len(f) == m);
vc<mint> a(m);
FOR(i, m) a[i] = v[1][m - i - 1] * (i + 1);
a = eval(a);
vc<vc<mint>> g(sz << 1);
FOR(i, sz) g[i + sz] = {(i < m ? f[i] / a[i] : 0)};
FOR_R(i, 1, sz) {
g[i] = convolution(g[i << 1], v[i << 1 | 1]);
Z tt = convolution(g[i << 1 | 1], v[i << 1]);
FOR(k, len(g[i])) g[i][k] += tt[k];
}
g[1].resize(m);
reverse(all(g[1]));
return g[1];
}
};
// O(Nlog^2N)
template <typename mint>
vc<mint> multi_eval_ntt(vc<mint> f, vc<mint> x) {
int n = 1, k = 0, sz = len(x);
while (n < sz) n <<= 1, ++k;
vc<vc<mint>> F(k + 1, vc<mint>(n << 1));
FOR(i, sz) F[0][i << 1] = -x[i];
FOR(d, k) {
int b = 1 << d;
FOR(L, 0, n << 1, b << 2) {
vc<mint> f = {F[d].begin() + L, F[d].begin() + L + b};
vc<mint> ff = {F[d].begin() + L + 2 * b, F[d].begin() + L + 3 * b};
ntt_db(f), ntt_db(ff);
FOR(i, b) f[i] += 1;
FOR(i, b) ff[i] += 1;
FOR(i, b, b << 1) f[i] -= 1;
FOR(i, b, b << 1) ff[i] -= 1;
copy(all(f), F[d].begin() + L);
copy(all(ff), F[d].begin() + L + 2 * b);
FOR(i, b << 1) F[d + 1][L + i] = f[i] * ff[i] - 1;
}
}
vc<mint> p = {F[k].begin(), F[k].begin() + n};
ntt(p, 1);
p.ep(1);
reverse(all(p));
p.resize(len(f));
p = fps_inv(p);
f.resize(n + len(p) - 1);
f = mid_prod(f, p);
reverse(all(f));
transposed_ntt(f, 1);
FOR_R(d, k) {
vc<mint> ff(n);
int b = 1 << d;
FOR(L, 0, n, b << 1) {
vc<mint> g(b << 1), gg(b << 1);
FOR(i, b << 1) g[i] = f[L + i] * F[d][2 * L + 2 * b + i];
FOR(i, b << 1) gg[i] = f[L + i] * F[d][2 * L + i];
ntt_db<mint, true>(g), ntt_db<mint, true>(gg);
FOR(i, b) ff[L + i] = g[i];
FOR(i, b) ff[L + b + i] = gg[i];
}
swap(f, ff);
}
f.resize(sz);
return f;
}
// O(Nlog^2N) ntt: 199 ms oth: 457 ms
template <typename mint>
vc<mint> multi_eval(const vc<mint> &f, const vc<mint> &x) {
if (f.empty()) return {};
if constexpr (mint::can_ntt()) return multi_eval_ntt(f, x);
subprod_tree g(x);
return g.eval(f);
}
template <typename mint>
vc<mint> multi_inte(const vc<mint> &x, const vc<mint> &y) {
if (x.empty()) return {};
subprod_tree g(x);
return g.inte(y);
}
// f(ar^k) k in [0, m) 点是等比数列可以 O(Nlog(N))
template <typename mint>
vc<mint> multi_eval_geoseq(vc<mint> f, mint a, mint r, int m) {
int n = len(f);
if (n == 0) return {};
Z eval = [&](mint x) -> mint {
mint fx = 0, c = 1;
FOR(i, n) fx += f[i] * c, c *= x;
return fx;
};
if (r == mint(0)) {
vc<mint> c(m);
FOR(i, 1, m) c[i] = f[0];
c[0] = eval(a);
return c;
}
if (n < 60 or m < 60) {
vc<mint> c(m);
FOR(i, m) c[i] = eval(a), a *= r;
return c;
}
assert(r != mint(0));
mint pw = 1;
FOR(i, n) f[i] *= pw, pw *= a;
Z ke = [&](mint r, int m) -> vc<mint> {
vc<mint> c(m);
mint pw = 1;
c[0] = 1;
FOR(i, m - 1) c[i + 1] = c[i] * pw, pw *= r;
return c;
};
vc<mint> A = ke(r, n + m - 1), B = ke(r.inv(), max(n, m));
FOR(i, n) f[i] *= B[i];
f = mid_prod(A, f);
FOR(i, m) f[i] *= B[i];
return f;
}
// y[i] = f(ar^i)
template <typename mint>
vc<mint> multi_inte_geoseq(vc<mint> y, mint a, mint r) {
int N = len(y);
if (N == 0) return {};
if (N == 1) return {y[0]};
assert(r != mint(0));
mint in = r.inv();
vc<mint> pw(2 * N - 1), tpw(2 * N - 1);
pw[0] = tpw[0] = mint(1);
FOR(i, 2 * N - 2) pw[i + 1] = pw[i] * r, tpw[i + 1] = tpw[i] * pw[i];
vc<mint> ipw(2 * N - 1), itpw(2 * N - 1);
ipw[0] = itpw[0] = mint(1);
FOR(i, N) ipw[i + 1] = ipw[i] * in, itpw[i + 1] = itpw[i] * ipw[i];
vc<mint> s(N);
s[0] = mint(1);
FOR(i, 1, N) s[i] = s[i - 1] * (mint(1) - pw[i]);
vc<mint> is = all_inv(s);
mint sn = s[N - 1] * (mint(1) - pw[N]);
FOR(i, N) {
y[i] = y[i] * tpw[N - i - 1] * itpw[N - 1] * is[i] * is[N - i - 1];
if (i & 1) y[i] = -y[i];
}
FOR(i, N) y[i] *= itpw[i];
vc<mint> f = mid_prod(tpw, y);
FOR(i, N) f[i] *= itpw[i];
vc<mint> g(N);
g[0] = mint(1);
FOR(i, 1, N) {
g[i] = tpw[i] * sn * is[i] * is[N - i];
if (i & 1) g[i] = -g[i];
}
f = convolution(f, g);
f.resize(N);
reverse(all(f));
mint ia = a.inv(), c = 1;
FOR(i, N) f[i] *= c, c *= ia;
return f;
}
#line 2 "YRS/po/multipoint_preprod.hpp"
#line 2 "YRS/po/conv_all.hpp"
#line 5 "YRS/po/conv_all.hpp"
// O(Nlog^2N) 总度数为 N ，即使fi度数很低，logfi度数也可能很大，试图用exp|log算会变成 NMlogN
template <typename mint>
vc<mint> conv_all(vc<vc<mint>> &f) {
if (f.empty()) return {{mint(1)}};
while (1) {
int N = len(f);
if (N == 1) break;
int m = (N + 1) >> 1;
FOR(i, m) {
if (i + i + 1 == N) f[i] = f[i << 1];
else f[i] = f[i << 1] * f[i << 1 | 1];
}
sh(f, m);
}
return f[0];
}
// product 1 - f[i]x
template <typename mint>
vc<mint> conv_all_1(vc<mint> f) {
if constexpr (not mint::can_ntt()) {
vc<vc<mint>> g;
for (Z &x : f) g.ep(vc<mint>({mint(1), -x}));
return conv_all(g);
}
int D = 6, N = 1, sz = len(f);
while (N < sz) N <<= 1;
int k = topbit(N);
vc<mint> F(N), nx(N);
FOR(i, sz) F[i] = -f[i];
FOR(d, k) {
int b = 1 << d;
if (d < D) {
fill(all(nx), mint(0));
FOR(L, 0, N, b << 1) {
FOR(i, b) FOR(j, b) nx[L + i + j] += F[L + i] * F[L + b + j];
FOR(i, b) nx[L + b + i] += F[L + i] + F[L + b + i];
}
} else if (d == D) {
FOR(L, 0, N, b << 1) {
vc<mint> f1 = {F.begin() + L, F.begin() + L + b};
vc<mint> f2 = {F.begin() + L + b, F.begin() + L + 2 * b};
sh(f1, b << 1), sh(f2, b << 1);
ntt(f1, 0), ntt(f2, 0);
FOR(i, b) nx[L + i] = f1[i] * f2[i] + f1[i] + f2[i];
FOR(i, b, b << 1) nx[L + i] = f1[i] * f2[i] - f1[i] - f2[i];
}
} else {
FOR(L, 0, N, b << 1) {
vc<mint> f1 = {F.begin() + L, F.begin() + L + b};
vc<mint> f2 = {F.begin() + L + b, F.begin() + L + 2 * b};
ntt_db(f1), ntt_db(f2);
FOR(i, b) nx[L + i] = f1[i] * f2[i] + f1[i] + f2[i];
FOR(i, b, b << 1) nx[L + i] = f1[i] * f2[i] - f1[i] - f2[i];
}
}
swap(F, nx);
}
if (k - 1 >= D) ntt(F, 1);
F.ep(1), reverse(all(F));
sh(F, sz + 1);
return F;
}
#line 2 "YRS/po/typical_divide.hpp"
#line 5 "YRS/po/typical_divide.hpp"
// given polynomial L_i, R_i, f.
// return [x^n]f(x)L(x)R(x)
// L(x) = prod{j<i}L_j(x)
// R(x) = prod{i<j}R_j(x)
// 没有set的位置初始化为 1
template <typename mint>
struct typical_divide_conquer {
using P = vc<mint>;
int N;
vc<P> A, B;
typical_divide_conquer(int N) : N(N), A(N), B(N) {}
void set_L(int i, P f) {
A[i] = f;
}
void set_R(int i, P f) {
B[i] = f;
}
P ke(int K, P f) {
if (N == 0) return {};
f.resize(K + 1);
vc<int> ls(N, -1), rs(N, -1);
vc<int> deg(N);
FOR(i, N) {
if (A[i].empty()) A[i] = {1};
if (B[i].empty()) B[i] = {1};
deg[i] = max(len(A[i]), len(B[i])) - 1;
A[i].resize(deg[i] + 1);
B[i].resize(deg[i] + 1);
}
Z dfs = [&](Z &dfs, int l, int r) -> int {
if (l + 1 == r) return l;
int m = (l + r) >> 1;
int a = dfs(dfs, l, m), b = dfs(dfs, m, r);
int x = len(ls);
ls.ep(a), rs.ep(b);
A.ep(A[a] * A[b]);
B.ep(B[a] * B[b]);
deg.ep(len(A.back()) - 1);
return x;
};
dfs(dfs, 0, N);
int rt = len(ls) - 1;
int d = deg[rt];
if (K < d) {
int ad = d - K;
vc<mint> g(len(f) + ad);
FOR(i, len(f)) g[ad + i] = f[i];
swap(f, g);
K = d;
}
if (K > d) {
int ls = K - d;
f = {f.begin() + ls, f.end()};
K = d;
}
reverse(all(f));
vc<mint> ans(N);
Z fs = [&](Z &fs, int k, P &g) -> void {
if (k < N) {
ans[k] = g[0];
return;
}
P g1 = mid_prod(g, B[rs[k]]);
P g2 = mid_prod(g, A[ls[k]]);
fs(fs, ls[k], g1), fs(fs, rs[k], g2);
};
fs(fs, rt, f);
return ans;
}
};
#line 6 "YRS/po/multipoint_preprod.hpp"
// 前缀乘积多项式多点求值
// F[0](point[i]) ... f[cnt[i] - 1](point[i])
template <typename mint>
vc<mint> multi_eval_preprod(vc<vc<mint>> F, vc<mint> x, vc<int> cnt) {
int N = len(x);
if (N == 0) return {};
vc<int> I = argsort(cnt);
x = rearrange(x, I);
cnt = rearrange(cnt, I);
vc<vc<mint>> G1, G2;
vc<vc<vc<mint>>> L(N), R(N);
FOR(i, N) {
vc<mint> f{mint(1), -x[i]};
L[i].ep(f), R[i].ep(f), G2.ep(f);
}
int K = 0;
for (Z &f : F) reverse(all(f));
FOR(i, cnt[0]) G1.ep(F[i]), K += len(F[i]) - 1;
FOR(j, N - 1) {
FOR(k, cnt[j], cnt[j + 1]) {
vc<mint> g(len(F[k]));
g.back() = 1;
L[j].ep(F[k]), R[j + 1].ep(g), K += len(g) - 1;
}
}
typical_divide_conquer<mint> seg(N);
FOR(i, N - 1) seg.set_L(i, conv_all(L[i]));
FOR(i, 1, N) seg.set_R(i, conv_all(R[i]));
vc<mint> g1 = conv_all(G1);
vc<mint> g2 = conv_all(G2);
g1.resize(K + 1), g2.resize(K + 1);
vc<mint> ans = seg.ke(K, fps_div(g1, g2));
I = argsort(I);
ans = rearrange(ans, I);
return ans;
}
#line 6 "YRS/po/f/factorials.hpp"
TE vc<T> factorials(vc<int> a) {
int N = len(a);
constexpr int B = 40000;
vc<T> fx = stiling_1_n<T>(B);
vc<T> st(B);
FOR(i, B) st[i] = T(1) + T(B) * T(i);
vc<T> devil = multi_eval(fx, st);
devil.insert(devil.begin(), T(1));
FOR(i, B) devil[i + 1] *= devil[i];
vc<vc<T>> polys(B);
FOR(i, B) polys[i] = {T(i), T(1)};
vc<T> p(N);
vc<int> c(N);
FOR(i, N) p[i] = st[a[i] / B], c[i] = a[i] % B;
Z ans = multi_eval_preprod(polys, p, c);
FOR(i, N) ans[i] *= devil[a[i] / B];
return ans;
}
#line 10 "No_148_\u8a66\u9a13\u76e3\u7763_3.cpp"
using mint = M17;
constexpr int mod = mint::get_mod();
void Yorisou() {
INT(Q);
vc<PLL> q;
FOR(Q) {
STR(C, P);
ll c = 0, p = 0;
for (char x : C) c = min<ll>(inf<int>, c * 10 + x - '0');
for (char x : P) p = min<ll>(inf<int>, p * 10 + x - '0');
q.ep(c, p);
}
vc<u8> vis(Q);
vc<int> x;
FOR(i, Q) {
Z [c, p] = q[i];
ll l = c - 2 * p + 2, r = c - p + 1;
if (p > mod) vis[i] = 1;
else if (ceil<ll>(l, mod) * mod <= r) vis[i] = 1;
else if (c < 2 * p - 1) vis[i] = 1;
else x.ep(l - 1), x.ep(r);
}
vc<mint> s = factorials<mint>(x);
int t = 0;
FOR(i, Q) {
if (vis[i]) print(0);
else print(s[t + 1] / s[t]), t += 2;
}
}
constexpr int tests = 0, fl = 0, DB = 10;
#line 1 "YRS/aa/main.hpp"
int main() {
cin.tie(nullptr)->sync_with_stdio(0);
int T = 1;
if (fl) cerr.tie(0);
if (tests and not fl) IN(T);
for (int i = 0; i < T or fl; ++i) {
Yorisou();
if (fl and i % DB == 0) cerr << "Case: " << i << '\n';
}
return 0;
}
#line 42 "No_148_\u8a66\u9a13\u76e3\u7763_3.cpp"