結果
| 問題 | No.2166 Paint and Fill |
| ユーザー |
 NyaanNyaan
|
| 提出日時 | 2022-11-22 00:48:56 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
RE
(最新)
AC
(最初)
|
| 実行時間 | - |
| コード長 | 44,508 bytes |
| コンパイル時間 | 7,524 ms |
| コンパイル使用メモリ | 328,536 KB |
| 実行使用メモリ | 82,176 KB |
| 最終ジャッジ日時 | 2024-11-17 07:45:04 |
| 合計ジャッジ時間 | 48,873 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge3 |
（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
6,820 KB |
| testcase_01 | RE | - |
| testcase_02 | AC | 397 ms
14,572 KB |
| testcase_03 | AC | 23 ms
6,820 KB |
| testcase_04 | AC | 23 ms
6,820 KB |
| testcase_05 | AC | 22 ms
6,816 KB |
| testcase_06 | AC | 22 ms
6,820 KB |
| testcase_07 | AC | 21 ms
6,816 KB |
| testcase_08 | AC | 1,144 ms
26,480 KB |
| testcase_09 | AC | 1,158 ms
26,748 KB |
| testcase_10 | AC | 1,196 ms
27,180 KB |
| testcase_11 | AC | 1,133 ms
26,580 KB |
| testcase_12 | AC | 1,110 ms
26,936 KB |
| testcase_13 | AC | 2,913 ms
40,624 KB |
| testcase_14 | AC | 3,035 ms
40,384 KB |
| testcase_15 | AC | 3,038 ms
40,276 KB |
| testcase_16 | AC | 2,988 ms
38,996 KB |
| testcase_17 | AC | 2,895 ms
39,320 KB |
| testcase_18 | AC | 2,776 ms
42,724 KB |
| testcase_19 | AC | 2,802 ms
42,780 KB |
| testcase_20 | AC | 2,616 ms
74,380 KB |
| testcase_21 | AC | 2,436 ms
75,712 KB |
| testcase_22 | AC | 1,475 ms
82,176 KB |
| testcase_23 | AC | 1,934 ms
53,480 KB |
| testcase_24 | AC | 1,770 ms
57,172 KB |
| testcase_25 | RE | - |
| testcase_26 | RE | - |
| testcase_27 | RE | - |
| testcase_28 | RE | - |
| testcase_29 | RE | - |
| testcase_30 | RE | - |
| testcase_31 | RE | - |
| testcase_32 | RE | - |
| testcase_33 | RE | - |
| testcase_34 | RE | - |
| testcase_35 | RE | - |
| testcase_36 | RE | - |
| testcase_37 | RE | - |
| testcase_38 | RE | - |
| testcase_39 | RE | - |
ソースコード
/**
* date : 2022-11-22 00:48:48
*/
#define NDEBUG
using namespace std;
// intrinstic
#include <immintrin.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
// utility
namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;
template <typename T, typename U>
struct P : pair<T, U> {
template <typename... Args>
P(Args... args) : pair<T, U>(args...) {}
using pair<T, U>::first;
using pair<T, U>::second;
P &operator+=(const P &r) {
first += r.first;
second += r.second;
return *this;
}
P &operator-=(const P &r) {
first -= r.first;
second -= r.second;
return *this;
}
P &operator*=(const P &r) {
first *= r.first;
second *= r.second;
return *this;
}
template <typename S>
P &operator*=(const S &r) {
first *= r, second *= r;
return *this;
}
P operator+(const P &r) const { return P(*this) += r; }
P operator-(const P &r) const { return P(*this) -= r; }
P operator*(const P &r) const { return P(*this) *= r; }
template <typename S>
P operator*(const S &r) const {
return P(*this) *= r;
}
P operator-() const { return P{-first, -second}; }
};
using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;
constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;
template <typename T>
int sz(const T &t) {
return t.size();
}
template <typename T, typename U>
inline bool amin(T &x, U y) {
return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
return (x < y) ? (x = y, true) : false;
}
template <typename T>
inline T Max(const vector<T> &v) {
return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
return accumulate(begin(v), end(v), 0LL);
}
template <typename T>
int lb(const vector<T> &v, const T &a) {
return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
return upper_bound(begin(v), end(v), a) - begin(v);
}
constexpr long long TEN(int n) {
long long ret = 1, x = 10;
for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
return ret;
}
template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
return make_pair(t, u);
}
template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
vector<T> ret(v.size() + 1);
if (rev) {
for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
} else {
for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
}
return ret;
};
template <typename T>
vector<T> mkuni(const vector<T> &v) {
vector<T> ret(v);
sort(ret.begin(), ret.end());
ret.erase(unique(ret.begin(), ret.end()), ret.end());
return ret;
}
template <typename F>
vector<int> mkord(int N,F f) {
vector<int> ord(N);
iota(begin(ord), end(ord), 0);
sort(begin(ord), end(ord), f);
return ord;
}
template <typename T>
vector<int> mkinv(vector<T> &v) {
int max_val = *max_element(begin(v), end(v));
vector<int> inv(max_val + 1, -1);
for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
return inv;
}
vector<int> mkiota(int n) {
vector<int> ret(n);
iota(begin(ret), end(ret), 0);
return ret;
}
template <typename T>
T mkrev(const T &v) {
T w{v};
reverse(begin(w), end(w));
return w;
}
template <typename T>
bool nxp(vector<T> &v) {
return next_permutation(begin(v), end(v));
}
template <typename T>
using minpq = priority_queue<T, vector<T>, greater<T>>;
} // namespace Nyaan
// bit operation
namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
return _mm_popcnt_u64(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
} // namespace Nyaan
// inout
namespace Nyaan {
template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
os << p.first << " " << p.second;
return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
is >> p.first >> p.second;
return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
int s = (int)v.size();
for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
for (auto &x : v) is >> x;
return is;
}
istream &operator>>(istream &is, __int128_t &x) {
string S;
is >> S;
x = 0;
int flag = 0;
for (auto &c : S) {
if (c == '-') {
flag = true;
continue;
}
x *= 10;
x += c - '0';
}
if (flag) x = -x;
return is;
}
istream &operator>>(istream &is, __uint128_t &x) {
string S;
is >> S;
x = 0;
for (auto &c : S) {
x *= 10;
x += c - '0';
}
return is;
}
ostream &operator<<(ostream &os, __int128_t x) {
if (x == 0) return os << 0;
if (x < 0) os << '-', x = -x;
string S;
while (x) S.push_back('0' + x % 10), x /= 10;
reverse(begin(S), end(S));
return os << S;
}
ostream &operator<<(ostream &os, __uint128_t x) {
if (x == 0) return os << 0;
string S;
while (x) S.push_back('0' + x % 10), x /= 10;
reverse(begin(S), end(S));
return os << S;
}
void in() {}
template <typename T, class... U>
void in(T &t, U &...u) {
cin >> t;
in(u...);
}
void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
cout << t;
if (sizeof...(u)) cout << sep;
out(u...);
}
void outr() {}
template <typename T, class... U, char sep = ' '>
void outr(const T &t, const U &...u) {
cout << t;
outr(u...);
}
struct IoSetupNya {
IoSetupNya() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(15);
cerr << fixed << setprecision(7);
}
} iosetupnya;
} // namespace Nyaan
// debug
#ifdef NyaanDebug
#define trc(...) (void(0))
#else
#define trc(...) (void(0))
#endif
#ifdef NyaanLocal
#define trc2(...) (void(0))
#else
#define trc2(...) (void(0))
#endif
// macro
#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#define ini(...) \
int __VA_ARGS__; \
in(__VA_ARGS__)
#define inl(...) \
long long __VA_ARGS__; \
in(__VA_ARGS__)
#define ins(...) \
string __VA_ARGS__; \
in(__VA_ARGS__)
#define in2(s, t) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i]); \
}
#define in3(s, t, u) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i], u[i]); \
}
#define in4(s, t, u, v) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i], u[i], v[i]); \
}
#define die(...) \
do { \
Nyaan::out(__VA_ARGS__); \
return; \
} while (0)
namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }
//
namespace my_rand {
using i64 = long long;
using u64 = unsigned long long;
// [0, 2^64 - 1)
u64 rng() {
static u64 _x =
u64(chrono::duration_cast<chrono::nanoseconds>(
chrono::high_resolution_clock::now().time_since_epoch())
.count()) *
10150724397891781847ULL;
_x ^= _x << 7;
return _x ^= _x >> 9;
}
// [l, r]
i64 rng(i64 l, i64 r) {
assert(l <= r);
return l + rng() % (r - l + 1);
}
// [l, r)
i64 randint(i64 l, i64 r) {
assert(l < r);
return l + rng() % (r - l);
}
// choose n numbers from [l, r) without overlapping
vector<i64> randset(i64 l, i64 r, i64 n) {
assert(l <= r && n <= r - l);
unordered_set<i64> s;
for (i64 i = n; i; --i) {
i64 m = randint(l, r + 1 - i);
if (s.find(m) != s.end()) m = r - i;
s.insert(m);
}
vector<i64> ret;
for (auto& x : s) ret.push_back(x);
return ret;
}
// [0.0, 1.0)
double rnd() { return rng() * 5.42101086242752217004e-20; }
template <typename T>
void randshf(vector<T>& v) {
int n = v.size();
for (int i = 1; i < n; i++) swap(v[i], v[randint(0, i + 1)]);
}
} // namespace my_rand
using my_rand::randint;
using my_rand::randset;
using my_rand::randshf;
using my_rand::rnd;
using my_rand::rng;
//
template <typename T, int H, int W>
struct Matrix {
using Array = array<array<T, W>, H>;
Array A;
Matrix() : A() {
for (int i = 0; i < H; i++)
for (int j = 0; j < W; j++) (*this)[i][j] = T();
}
int height() const { return H; }
int width() const { return W; }
inline const array<T, W> &operator[](int k) const { return A[k]; }
inline array<T, W> &operator[](int k) { return A[k]; }
static Matrix I() {
assert(H == W);
Matrix mat;
for (int i = 0; i < H; i++) mat[i][i] = 1;
return (mat);
}
Matrix &operator+=(const Matrix &B) {
for (int i = 0; i < H; i++)
for (int j = 0; j < W; j++) A[i][j] += B[i][j];
return (*this);
}
Matrix &operator-=(const Matrix &B) {
for (int i = 0; i < H; i++)
for (int j = 0; j < W; j++) A[i][j] -= B[i][j];
return (*this);
}
Matrix &operator*=(const Matrix &B) {
assert(H == W);
Matrix C;
for (int i = 0; i < H; i++)
for (int k = 0; k < H; k++)
for (int j = 0; j < H; j++) C[i][j] += A[i][k] * B[k][j];
A.swap(C.A);
return (*this);
}
Matrix &operator^=(long long k) {
Matrix B = Matrix::I();
while (k > 0) {
if (k & 1) B *= *this;
*this *= *this;
k >>= 1LL;
}
A.swap(B.A);
return (*this);
}
Matrix operator+(const Matrix &B) const { return (Matrix(*this) += B); }
Matrix operator-(const Matrix &B) const { return (Matrix(*this) -= B); }
Matrix operator*(const Matrix &B) const { return (Matrix(*this) *= B); }
Matrix operator^(const long long k) const { return (Matrix(*this) ^= k); }
bool operator==(const Matrix &B) const {
for (int i = 0; i < H; i++)
for (int j = 0; j < W; j++)
if (A[i][j] != B[i][j]) return false;
return true;
}
bool operator!=(const Matrix &B) const {
for (int i = 0; i < H; i++)
for (int j = 0; j < W; j++)
if (A[i][j] != B[i][j]) return true;
return false;
}
friend ostream &operator<<(ostream &os,const Matrix &p) {
for (int i = 0; i < H; i++) {
os << "[";
for (int j = 0; j < W; j++) {
os << p[i][j] << (j + 1 == W ? "]\n" : ",");
}
}
return (os);
}
T determinant(int n = -1) {
if (n == -1) n = H;
Matrix B(*this);
T ret = 1;
for (int i = 0; i < n; i++) {
int idx = -1;
for (int j = i; j < n; j++) {
if (B[j][i] != 0) {
idx = j;
break;
}
}
if (idx == -1) return 0;
if (i != idx) {
ret *= T(-1);
swap(B[i], B[idx]);
}
ret *= B[i][i];
T inv = T(1) / B[i][i];
for (int j = 0; j < n; j++) {
B[i][j] *= inv;
}
for (int j = i + 1; j < n; j++) {
T a = B[j][i];
if (a == 0) continue;
for (int k = i; k < n; k++) {
B[j][k] -= B[i][k] * a;
}
}
}
return (ret);
}
};
/**
* @brief 行列ライブラリ(std::array版)
*/
//
template <uint32_t mod>
struct LazyMontgomeryModInt {
using mint = LazyMontgomeryModInt;
using i32 = int32_t;
using u32 = uint32_t;
using u64 = uint64_t;
static constexpr u32 get_r() {
u32 ret = mod;
for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
return ret;
}
static constexpr u32 r = get_r();
static constexpr u32 n2 = -u64(mod) % mod;
static_assert(r * mod == 1, "invalid, r * mod != 1");
static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");
static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");
u32 a;
constexpr LazyMontgomeryModInt() : a(0) {}
constexpr LazyMontgomeryModInt(const int64_t &b)
: a(reduce(u64(b % mod + mod) * n2)){};
static constexpr u32 reduce(const u64 &b) {
return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
}
constexpr mint &operator+=(const mint &b) {
if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
return *this;
}
constexpr mint &operator-=(const mint &b) {
if (i32(a -= b.a) < 0) a += 2 * mod;
return *this;
}
constexpr mint &operator*=(const mint &b) {
a = reduce(u64(a) * b.a);
return *this;
}
constexpr mint &operator/=(const mint &b) {
*this *= b.inverse();
return *this;
}
constexpr mint operator+(const mint &b) const { return mint(*this) += b; }
constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }
constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }
constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }
constexpr bool operator==(const mint &b) const {
return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
}
constexpr bool operator!=(const mint &b) const {
return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
}
constexpr mint operator-() const { return mint() - mint(*this); }
constexpr mint pow(u64 n) const {
mint ret(1), mul(*this);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
constexpr mint inverse() const { return pow(mod - 2); }
friend ostream &operator<<(ostream &os, const mint &b) {
return os << b.get();
}
friend istream &operator>>(istream &is, mint &b) {
int64_t t;
is >> t;
b = LazyMontgomeryModInt<mod>(t);
return (is);
}
constexpr u32 get() const {
u32 ret = reduce(a);
return ret >= mod ? ret - mod : ret;
}
static constexpr u32 get_mod() { return mod; }
};
template <typename mint>
struct NTT {
static constexpr uint32_t get_pr() {
uint32_t _mod = mint::get_mod();
using u64 = uint64_t;
u64 ds[32] = {};
int idx = 0;
u64 m = _mod - 1;
for (u64 i = 2; i * i <= m; ++i) {
if (m % i == 0) {
ds[idx++] = i;
while (m % i == 0) m /= i;
}
}
if (m != 1) ds[idx++] = m;
uint32_t _pr = 2;
while (1) {
int flg = 1;
for (int i = 0; i < idx; ++i) {
u64 a = _pr, b = (_mod - 1) / ds[i], r = 1;
while (b) {
if (b & 1) r = r * a % _mod;
a = a * a % _mod;
b >>= 1;
}
if (r == 1) {
flg = 0;
break;
}
}
if (flg == 1) break;
++_pr;
}
return _pr;
};
static constexpr uint32_t mod = mint::get_mod();
static constexpr uint32_t pr = get_pr();
static constexpr int level = __builtin_ctzll(mod - 1);
mint dw[level], dy[level];
void setwy(int k) {
mint w[level], y[level];
w[k - 1] = mint(pr).pow((mod - 1) / (1 << k));
y[k - 1] = w[k - 1].inverse();
for (int i = k - 2; i > 0; --i)
w[i] = w[i + 1] * w[i + 1], y[i] = y[i + 1] * y[i + 1];
dw[1] = w[1], dy[1] = y[1], dw[2] = w[2], dy[2] = y[2];
for (int i = 3; i < k; ++i) {
dw[i] = dw[i - 1] * y[i - 2] * w[i];
dy[i] = dy[i - 1] * w[i - 2] * y[i];
}
}
NTT() { setwy(level); }
void fft4(vector<mint> &a, int k) {
if ((int)a.size() <= 1) return;
if (k == 1) {
mint a1 = a[1];
a[1] = a[0] - a[1];
a[0] = a[0] + a1;
return;
}
if (k & 1) {
int v = 1 << (k - 1);
for (int j = 0; j < v; ++j) {
mint ajv = a[j + v];
a[j + v] = a[j] - ajv;
a[j] += ajv;
}
}
int u = 1 << (2 + (k & 1));
int v = 1 << (k - 2 - (k & 1));
mint one = mint(1);
mint imag = dw[1];
while (v) {
// jh = 0
{
int j0 = 0;
int j1 = v;
int j2 = j1 + v;
int j3 = j2 + v;
for (; j0 < v; ++j0, ++j1, ++j2, ++j3) {
mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];
mint t0p2 = t0 + t2, t1p3 = t1 + t3;
mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;
a[j0] = t0p2 + t1p3, a[j1] = t0p2 - t1p3;
a[j2] = t0m2 + t1m3, a[j3] = t0m2 - t1m3;
}
}
// jh >= 1
mint ww = one, xx = one * dw[2], wx = one;
for (int jh = 4; jh < u;) {
ww = xx * xx, wx = ww * xx;
int j0 = jh * v;
int je = j0 + v;
int j2 = je + v;
for (; j0 < je; ++j0, ++j2) {
mint t0 = a[j0], t1 = a[j0 + v] * xx, t2 = a[j2] * ww,
t3 = a[j2 + v] * wx;
mint t0p2 = t0 + t2, t1p3 = t1 + t3;
mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;
a[j0] = t0p2 + t1p3, a[j0 + v] = t0p2 - t1p3;
a[j2] = t0m2 + t1m3, a[j2 + v] = t0m2 - t1m3;
}
xx *= dw[__builtin_ctzll((jh += 4))];
}
u <<= 2;
v >>= 2;
}
}
void ifft4(vector<mint> &a, int k) {
if ((int)a.size() <= 1) return;
if (k == 1) {
mint a1 = a[1];
a[1] = a[0] - a[1];
a[0] = a[0] + a1;
return;
}
int u = 1 << (k - 2);
int v = 1;
mint one = mint(1);
mint imag = dy[1];
while (u) {
// jh = 0
{
int j0 = 0;
int j1 = v;
int j2 = v + v;
int j3 = j2 + v;
for (; j0 < v; ++j0, ++j1, ++j2, ++j3) {
mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];
mint t0p1 = t0 + t1, t2p3 = t2 + t3;
mint t0m1 = t0 - t1, t2m3 = (t2 - t3) * imag;
a[j0] = t0p1 + t2p3, a[j2] = t0p1 - t2p3;
a[j1] = t0m1 + t2m3, a[j3] = t0m1 - t2m3;
}
}
// jh >= 1
mint ww = one, xx = one * dy[2], yy = one;
u <<= 2;
for (int jh = 4; jh < u;) {
ww = xx * xx, yy = xx * imag;
int j0 = jh * v;
int je = j0 + v;
int j2 = je + v;
for (; j0 < je; ++j0, ++j2) {
mint t0 = a[j0], t1 = a[j0 + v], t2 = a[j2], t3 = a[j2 + v];
mint t0p1 = t0 + t1, t2p3 = t2 + t3;
mint t0m1 = (t0 - t1) * xx, t2m3 = (t2 - t3) * yy;
a[j0] = t0p1 + t2p3, a[j2] = (t0p1 - t2p3) * ww;
a[j0 + v] = t0m1 + t2m3, a[j2 + v] = (t0m1 - t2m3) * ww;
}
xx *= dy[__builtin_ctzll(jh += 4)];
}
u >>= 4;
v <<= 2;
}
if (k & 1) {
u = 1 << (k - 1);
for (int j = 0; j < u; ++j) {
mint ajv = a[j] - a[j + u];
a[j] += a[j + u];
a[j + u] = ajv;
}
}
}
void ntt(vector<mint> &a) {
if ((int)a.size() <= 1) return;
fft4(a, __builtin_ctz(a.size()));
}
void intt(vector<mint> &a) {
if ((int)a.size() <= 1) return;
ifft4(a, __builtin_ctz(a.size()));
mint iv = mint(a.size()).inverse();
for (auto &x : a) x *= iv;
}
vector<mint> multiply(const vector<mint> &a, const vector<mint> &b) {
int l = a.size() + b.size() - 1;
if (min<int>(a.size(), b.size()) <= 40) {
vector<mint> s(l);
for (int i = 0; i < (int)a.size(); ++i)
for (int j = 0; j < (int)b.size(); ++j) s[i + j] += a[i] * b[j];
return s;
}
int k = 2, M = 4;
while (M < l) M <<= 1, ++k;
setwy(k);
vector<mint> s(M), t(M);
for (int i = 0; i < (int)a.size(); ++i) s[i] = a[i];
for (int i = 0; i < (int)b.size(); ++i) t[i] = b[i];
fft4(s, k);
fft4(t, k);
for (int i = 0; i < M; ++i) s[i] *= t[i];
ifft4(s, k);
s.resize(l);
mint invm = mint(M).inverse();
for (int i = 0; i < l; ++i) s[i] *= invm;
return s;
}
void ntt_doubling(vector<mint> &a) {
int M = (int)a.size();
auto b = a;
intt(b);
mint r = 1, zeta = mint(pr).pow((mint::get_mod() - 1) / (M << 1));
for (int i = 0; i < M; i++) b[i] *= r, r *= zeta;
ntt(b);
copy(begin(b), end(b), back_inserter(a));
}
};
template <typename mint>
struct FormalPowerSeries : vector<mint> {
using vector<mint>::vector;
using FPS = FormalPowerSeries;
FPS &operator+=(const FPS &r) {
if (r.size() > this->size()) this->resize(r.size());
for (int i = 0; i < (int)r.size(); i++) (*this)[i] += r[i];
return *this;
}
FPS &operator+=(const mint &r) {
if (this->empty()) this->resize(1);
(*this)[0] += r;
return *this;
}
FPS &operator-=(const FPS &r) {
if (r.size() > this->size()) this->resize(r.size());
for (int i = 0; i < (int)r.size(); i++) (*this)[i] -= r[i];
return *this;
}
FPS &operator-=(const mint &r) {
if (this->empty()) this->resize(1);
(*this)[0] -= r;
return *this;
}
FPS &operator*=(const mint &v) {
for (int k = 0; k < (int)this->size(); k++) (*this)[k] *= v;
return *this;
}
FPS &operator/=(const FPS &r) {
if (this->size() < r.size()) {
this->clear();
return *this;
}
int n = this->size() - r.size() + 1;
if ((int)r.size() <= 64) {
FPS f(*this), g(r);
g.shrink();
mint coeff = g.back().inverse();
for (auto &x : g) x *= coeff;
int deg = (int)f.size() - (int)g.size() + 1;
int gs = g.size();
FPS quo(deg);
for (int i = deg - 1; i >= 0; i--) {
quo[i] = f[i + gs - 1];
for (int j = 0; j < gs; j++) f[i + j] -= quo[i] * g[j];
}
*this = quo * coeff;
this->resize(n, mint(0));
return *this;
}
return *this = ((*this).rev().pre(n) * r.rev().inv(n)).pre(n).rev();
}
FPS &operator%=(const FPS &r) {
*this -= *this / r * r;
shrink();
return *this;
}
FPS operator+(const FPS &r) const { return FPS(*this) += r; }
FPS operator+(const mint &v) const { return FPS(*this) += v; }
FPS operator-(const FPS &r) const { return FPS(*this) -= r; }
FPS operator-(const mint &v) const { return FPS(*this) -= v; }
FPS operator*(const FPS &r) const { return FPS(*this) *= r; }
FPS operator*(const mint &v) const { return FPS(*this) *= v; }
FPS operator/(const FPS &r) const { return FPS(*this) /= r; }
FPS operator%(const FPS &r) const { return FPS(*this) %= r; }
FPS operator-() const {
FPS ret(this->size());
for (int i = 0; i < (int)this->size(); i++) ret[i] = -(*this)[i];
return ret;
}
void shrink() {
while (this->size() && this->back() == mint(0)) this->pop_back();
}
FPS rev() const {
FPS ret(*this);
reverse(begin(ret), end(ret));
return ret;
}
FPS dot(FPS r) const {
FPS ret(min(this->size(), r.size()));
for (int i = 0; i < (int)ret.size(); i++) ret[i] = (*this)[i] * r[i];
return ret;
}
FPS pre(int sz) const {
return FPS(begin(*this), begin(*this) + min((int)this->size(), sz));
}
FPS operator>>(int sz) const {
if ((int)this->size() <= sz) return {};
FPS ret(*this);
ret.erase(ret.begin(), ret.begin() + sz);
return ret;
}
FPS operator<<(int sz) const {
FPS ret(*this);
ret.insert(ret.begin(), sz, mint(0));
return ret;
}
FPS diff() const {
const int n = (int)this->size();
FPS ret(max(0, n - 1));
mint one(1), coeff(1);
for (int i = 1; i < n; i++) {
ret[i - 1] = (*this)[i] * coeff;
coeff += one;
}
return ret;
}
FPS integral() const {
const int n = (int)this->size();
FPS ret(n + 1);
ret[0] = mint(0);
if (n > 0) ret[1] = mint(1);
auto mod = mint::get_mod();
for (int i = 2; i <= n; i++) ret[i] = (-ret[mod % i]) * (mod / i);
for (int i = 0; i < n; i++) ret[i + 1] *= (*this)[i];
return ret;
}
mint eval(mint x) const {
mint r = 0, w = 1;
for (auto &v : *this) r += w * v, w *= x;
return r;
}
FPS log(int deg = -1) const {
assert((*this)[0] == mint(1));
if (deg == -1) deg = (int)this->size();
return (this->diff() * this->inv(deg)).pre(deg - 1).integral();
}
FPS pow(int64_t k, int deg = -1) const {
const int n = (int)this->size();
if (deg == -1) deg = n;
if (k == 0) {
FPS ret(deg);
if (deg) ret[0] = 1;
return ret;
}
for (int i = 0; i < n; i++) {
if ((*this)[i] != mint(0)) {
mint rev = mint(1) / (*this)[i];
FPS ret = (((*this * rev) >> i).log(deg) * k).exp(deg);
ret *= (*this)[i].pow(k);
ret = (ret << (i * k)).pre(deg);
if ((int)ret.size() < deg) ret.resize(deg, mint(0));
return ret;
}
if (__int128_t(i + 1) * k >= deg) return FPS(deg, mint(0));
}
return FPS(deg, mint(0));
}
static void *ntt_ptr;
static void set_fft();
FPS &operator*=(const FPS &r);
void ntt();
void intt();
void ntt_doubling();
static int ntt_pr();
FPS inv(int deg = -1) const;
FPS exp(int deg = -1) const;
};
template <typename mint>
void *FormalPowerSeries<mint>::ntt_ptr = nullptr;
/**
* @brief 多項式/形式的冪級数ライブラリ
* @docs docs/fps/formal-power-series.md
*/
template <typename mint>
void FormalPowerSeries<mint>::set_fft() {
if (!ntt_ptr) ntt_ptr = new NTT<mint>;
}
template <typename mint>
FormalPowerSeries<mint>& FormalPowerSeries<mint>::operator*=(
const FormalPowerSeries<mint>& r) {
if (this->empty() || r.empty()) {
this->clear();
return *this;
}
set_fft();
auto ret = static_cast<NTT<mint>*>(ntt_ptr)->multiply(*this, r);
return *this = FormalPowerSeries<mint>(ret.begin(), ret.end());
}
template <typename mint>
void FormalPowerSeries<mint>::ntt() {
set_fft();
static_cast<NTT<mint>*>(ntt_ptr)->ntt(*this);
}
template <typename mint>
void FormalPowerSeries<mint>::intt() {
set_fft();
static_cast<NTT<mint>*>(ntt_ptr)->intt(*this);
}
template <typename mint>
void FormalPowerSeries<mint>::ntt_doubling() {
set_fft();
static_cast<NTT<mint>*>(ntt_ptr)->ntt_doubling(*this);
}
template <typename mint>
int FormalPowerSeries<mint>::ntt_pr() {
set_fft();
return static_cast<NTT<mint>*>(ntt_ptr)->pr;
}
template <typename mint>
FormalPowerSeries<mint> FormalPowerSeries<mint>::inv(int deg) const {
assert((*this)[0] != mint(0));
if (deg == -1) deg = (int)this->size();
FormalPowerSeries<mint> res(deg);
res[0] = {mint(1) / (*this)[0]};
for (int d = 1; d < deg; d <<= 1) {
FormalPowerSeries<mint> f(2 * d), g(2 * d);
for (int j = 0; j < min((int)this->size(), 2 * d); j++) f[j] = (*this)[j];
for (int j = 0; j < d; j++) g[j] = res[j];
f.ntt();
g.ntt();
for (int j = 0; j < 2 * d; j++) f[j] *= g[j];
f.intt();
for (int j = 0; j < d; j++) f[j] = 0;
f.ntt();
for (int j = 0; j < 2 * d; j++) f[j] *= g[j];
f.intt();
for (int j = d; j < min(2 * d, deg); j++) res[j] = -f[j];
}
return res.pre(deg);
}
template <typename mint>
FormalPowerSeries<mint> FormalPowerSeries<mint>::exp(int deg) const {
using fps = FormalPowerSeries<mint>;
assert((*this).size() == 0 || (*this)[0] == mint(0));
if (deg == -1) deg = this->size();
fps inv;
inv.reserve(deg + 1);
inv.push_back(mint(0));
inv.push_back(mint(1));
auto inplace_integral = [&](fps& F) -> void {
const int n = (int)F.size();
auto mod = mint::get_mod();
while ((int)inv.size() <= n) {
int i = inv.size();
inv.push_back((-inv[mod % i]) * (mod / i));
}
F.insert(begin(F), mint(0));
for (int i = 1; i <= n; i++) F[i] *= inv[i];
};
auto inplace_diff = [](fps& F) -> void {
if (F.empty()) return;
F.erase(begin(F));
mint coeff = 1, one = 1;
for (int i = 0; i < (int)F.size(); i++) {
F[i] *= coeff;
coeff += one;
}
};
fps b{1, 1 < (int)this->size() ? (*this)[1] : 0}, c{1}, z1, z2{1, 1};
for (int m = 2; m < deg; m *= 2) {
auto y = b;
y.resize(2 * m);
y.ntt();
z1 = z2;
fps z(m);
for (int i = 0; i < m; ++i) z[i] = y[i] * z1[i];
z.intt();
fill(begin(z), begin(z) + m / 2, mint(0));
z.ntt();
for (int i = 0; i < m; ++i) z[i] *= -z1[i];
z.intt();
c.insert(end(c), begin(z) + m / 2, end(z));
z2 = c;
z2.resize(2 * m);
z2.ntt();
fps x(begin(*this), begin(*this) + min<int>(this->size(), m));
x.resize(m);
inplace_diff(x);
x.push_back(mint(0));
x.ntt();
for (int i = 0; i < m; ++i) x[i] *= y[i];
x.intt();
x -= b.diff();
x.resize(2 * m);
for (int i = 0; i < m - 1; ++i) x[m + i] = x[i], x[i] = mint(0);
x.ntt();
for (int i = 0; i < 2 * m; ++i) x[i] *= z2[i];
x.intt();
x.pop_back();
inplace_integral(x);
for (int i = m; i < min<int>(this->size(), 2 * m); ++i) x[i] += (*this)[i];
fill(begin(x), begin(x) + m, mint(0));
x.ntt();
for (int i = 0; i < 2 * m; ++i) x[i] *= y[i];
x.intt();
b.insert(end(b), begin(x) + m, end(x));
}
return fps{begin(b), begin(b) + deg};
}
/**
* @brief NTT mod用FPSライブラリ
* @docs docs/fps/ntt-friendly-fps.md
*/
template <typename mint>
vector<mint> FastMultiEval(const FormalPowerSeries<mint> &f,
const vector<mint> &xs) {
using fps = FormalPowerSeries<mint>;
int s = xs.size();
int N = 1 << (32 - __builtin_clz((int)xs.size() - 1));
if(f.empty() || xs.empty()) return vector<mint>(s, mint(0));
vector<FormalPowerSeries<mint>> buf(2 * N);
for (int i = 0; i < N; i++) {
mint n = mint{i < s ? -xs[i] : mint(0)};
buf[i + N] = fps{n + 1, n - 1};
}
for (int i = N - 1; i > 0; i--) {
fps &g(buf[(i << 1) | 0]), &h(buf[(i << 1) | 1]);
int n = g.size();
int m = n << 1;
buf[i].reserve(m);
buf[i].resize(n);
for (int j = 0; j < n; j++) buf[i][j] = g[j] * h[j] - mint(1);
if (i != 1) {
buf[i].ntt_doubling();
for (int j = 0; j < m; j++) buf[i][j] += j < n ? mint(1) : -mint(1);
}
}
int fs = f.size();
fps root = buf[1];
root.intt();
root.push_back(1);
reverse(begin(root), end(root));
root = root.inv(fs).rev() * f;
root.erase(begin(root), begin(root) + fs - 1);
root.resize(N, mint(0));
vector<mint> ans(s);
auto calc = [&](auto rec, int i, int l, int r, fps g) -> void {
if (i >= N) {
ans[i - N] = g[0];
return;
}
int len = g.size(), m = (l + r) >> 1;
g.ntt();
fps tmp = buf[i * 2 + 1];
for (int j = 0; j < len; j++) tmp[j] *= g[j];
tmp.intt();
rec(rec, i * 2 + 0, l, m, fps{begin(tmp) + (len >> 1), end(tmp)});
if (m >= s) return;
tmp = buf[i * 2 + 0];
for (int j = 0; j < len; j++) tmp[j] *= g[j];
tmp.intt();
rec(rec, i * 2 + 1, m, r, fps{begin(tmp) + (len >> 1), end(tmp)});
};
calc(calc, 1, 0, N, root);
return ans;
}
/**
* @brief Multipoint Evaluation(高速化版)
*/
template <typename mint>
struct ProductTree {
using fps = FormalPowerSeries<mint>;
const vector<mint> &xs;
vector<fps> buf;
int N, xsz;
vector<int> l, r;
ProductTree(const vector<mint> &xs_) : xs(xs_), xsz(xs.size()) {
N = 1;
while (N < (int)xs.size()) N *= 2;
buf.resize(2 * N);
l.resize(2 * N, xs.size());
r.resize(2 * N, xs.size());
fps::set_fft();
if (fps::ntt_ptr == nullptr)
build();
else
build_ntt();
}
void build() {
for (int i = 0; i < xsz; i++) {
l[i + N] = i;
r[i + N] = i + 1;
buf[i + N] = {-xs[i], 1};
}
for (int i = N - 1; i > 0; i--) {
l[i] = l[(i << 1) | 0];
r[i] = r[(i << 1) | 1];
if (buf[(i << 1) | 0].empty())
continue;
else if (buf[(i << 1) | 1].empty())
buf[i] = buf[(i << 1) | 0];
else
buf[i] = buf[(i << 1) | 0] * buf[(i << 1) | 1];
}
}
void build_ntt() {
fps f;
f.reserve(N * 2);
for (int i = 0; i < xsz; i++) {
l[i + N] = i;
r[i + N] = i + 1;
buf[i + N] = {-xs[i] + 1, -xs[i] - 1};
}
for (int i = N - 1; i > 0; i--) {
l[i] = l[(i << 1) | 0];
r[i] = r[(i << 1) | 1];
if (buf[(i << 1) | 0].empty())
continue;
else if (buf[(i << 1) | 1].empty())
buf[i] = buf[(i << 1) | 0];
else if (buf[(i << 1) | 0].size() == buf[(i << 1) | 1].size()) {
buf[i] = buf[(i << 1) | 0];
f.clear();
copy(begin(buf[(i << 1) | 1]), end(buf[(i << 1) | 1]),
back_inserter(f));
buf[i].ntt_doubling();
f.ntt_doubling();
for (int j = 0; j < (int)buf[i].size(); j++) buf[i][j] *= f[j];
} else {
buf[i] = buf[(i << 1) | 0];
f.clear();
copy(begin(buf[(i << 1) | 1]), end(buf[(i << 1) | 1]),
back_inserter(f));
buf[i].ntt_doubling();
f.intt();
f.resize(buf[i].size(), mint(0));
f.ntt();
for (int j = 0; j < (int)buf[i].size(); j++) buf[i][j] *= f[j];
}
}
for (int i = 0; i < 2 * N; i++) {
buf[i].intt();
buf[i].shrink();
}
}
};
template <typename mint>
vector<mint> InnerMultipointEvaluation(const FormalPowerSeries<mint> &f,
const vector<mint> &xs,
const ProductTree<mint> &ptree) {
using fps = FormalPowerSeries<mint>;
vector<mint> ret;
ret.reserve(xs.size());
auto rec = [&](auto self, fps a, int idx) {
if (ptree.l[idx] == ptree.r[idx]) return;
a %= ptree.buf[idx];
if ((int)a.size() <= 64) {
for (int i = ptree.l[idx]; i < ptree.r[idx]; i++)
ret.push_back(a.eval(xs[i]));
return;
}
self(self, a, (idx << 1) | 0);
self(self, a, (idx << 1) | 1);
};
rec(rec, f, 1);
return ret;
}
template <typename mint>
vector<mint> MultipointEvaluation(const FormalPowerSeries<mint> &f,
const vector<mint> &xs) {
if(f.empty() || xs.empty()) return vector<mint>(xs.size(), mint(0));
return InnerMultipointEvaluation(f, xs, ProductTree<mint>(xs));
}
/**
* @brief Multipoint Evaluation
*/
//
template <typename T>
struct Binomial {
vector<T> f, g, h;
Binomial(int MAX = 0) {
assert(T::get_mod() != 0 && "Binomial<mint>()");
f.resize(1, T{1});
g.resize(1, T{1});
h.resize(1, T{1});
while (MAX >= (int)f.size()) extend();
}
void extend() {
int n = f.size();
int m = n * 2;
f.resize(m);
g.resize(m);
h.resize(m);
for (int i = n; i < m; i++) f[i] = f[i - 1] * T(i);
g[m - 1] = f[m - 1].inverse();
h[m - 1] = g[m - 1] * f[m - 2];
for (int i = m - 2; i >= n; i--) {
g[i] = g[i + 1] * T(i + 1);
h[i] = g[i] * f[i - 1];
}
}
T fac(int i) {
if (i < 0) return T(0);
while (i >= (int)f.size()) extend();
return f[i];
}
T finv(int i) {
if (i < 0) return T(0);
while (i >= (int)g.size()) extend();
return g[i];
}
T inv(int i) {
if (i < 0) return -inv(-i);
while (i >= (int)h.size()) extend();
return h[i];
}
T C(int n, int r) {
if (n < 0 || n < r || r < 0) return T(0);
return fac(n) * finv(n - r) * finv(r);
}
inline T operator()(int n, int r) { return C(n, r); }
template <typename I>
T multinomial(const vector<I>& r) {
static_assert(is_integral<I>::value == true);
int n = 0;
for (auto& x : r) {
if (x < 0) return T(0);
n += x;
}
T res = fac(n);
for (auto& x : r) res *= finv(x);
return res;
}
template <typename I>
T operator()(const vector<I>& r) {
return multinomial(r);
}
T C_naive(int n, int r) {
if (n < 0 || n < r || r < 0) return T(0);
T ret = T(1);
r = min(r, n - r);
for (int i = 1; i <= r; ++i) ret *= inv(i) * (n--);
return ret;
}
T P(int n, int r) {
if (n < 0 || n < r || r < 0) return T(0);
return fac(n) * finv(n - r);
}
T H(int n, int r) {
if (n < 0 || r < 0) return T(0);
return r == 0 ? 1 : C(n + r - 1, r);
}
};
template <typename mint>
FormalPowerSeries<mint> Pi(vector<FormalPowerSeries<mint>> v) {
using fps = FormalPowerSeries<mint>;
if ((int)v.size() == 0) return fps{mint(1)};
sort(begin(v), end(v), [](fps& a, fps& b) { return a.size() < b.size(); });
queue<fps> q;
for (auto& f : v) q.push(f);
while ((int)q.size() > 1) {
fps a = q.front();
q.pop();
fps b = q.front();
q.pop();
q.push(a * b);
}
return q.front();
}
template <typename mint>
void OGFtoEGF(FormalPowerSeries<mint>& f, Binomial<mint>& C) {
for (int i = 0; i < (int)f.size(); i++) f[i] *= C.finv(i);
}
template <typename mint>
void EGFtoOGF(FormalPowerSeries<mint>& f, Binomial<mint>& C) {
for (int i = 0; i < (int)f.size(); i++) f[i] *= C.fac(i);
}
template <typename mint>
FormalPowerSeries<mint> e_x(int deg, Binomial<mint>& C) {
while ((int)C.g.size() < deg) C.extend();
FormalPowerSeries<mint> ret{begin(C.g), begin(C.g) + deg};
return ret;
}
// f *= (1 + c x^n)
template <typename mint>
void sparse_mul(FormalPowerSeries<mint>& f, int n, mint c, int expand = true) {
if (expand) f.resize(f.size() + n);
for (int i = (int)f.size() - 1; i >= 0; --i) {
if (i - n >= 0) f[i] += f[i - n] * c;
}
}
// f /= (1 + c x^n)
template <typename mint>
void sparse_div(FormalPowerSeries<mint>& f, int n, mint c) {
for (int i = 0; i < (int)f.size(); ++i) {
if (i + n < (int)f.size()) f[i + n] -= f[i] * c;
}
}
//
using namespace Nyaan;
using mint = LazyMontgomeryModInt<998244353>;
using vm = vector<mint>;
using vvm = vector<vm>;
Binomial<mint> C;
using fps = FormalPowerSeries<mint>;
using namespace Nyaan;
// [x^k] (2 + 4x + x^2)^N
mint naive1(ll n, ll k) {
fps f(max<ll>(k + 1, 3));
f[0] = 2, f[1] = 4, f[2] = 1;
return f.pow(n)[k] * C.fac(k);
}
// [x^k] (2 + 4x + x^2)^N
mint naive2(ll n, ll k) {
if (k == 0) return mint{2}.pow(n);
fps f(k + 1);
f[0] = mint{2}.pow(n);
f[1] = f[0] * n * 2;
for (int a = 2; a <= k; a++) {
f[a] += f[a - 1] * 4 * (n + 1 - a) * C.inv(2);
f[a] += f[a - 2] * (2 * n + 2 - a) * (a - 1) * C.inv(2);
}
return f[k];
}
void test1() {
rep1(N, 30) rep(K, 2 * N + 1) {
mint ans1 = naive1(N, K);
mint ans2 = naive2(N, K);
if (ans1 != ans2) {
trc(N, K, ans1, ans2);
exit(1);
}
}
trc2("OK");
}
vm naive3(vl ns, vl ks) {
vm res;
int S = sz(ns);
rep(i, S) { res.push_back(naive2(ns[i], ks[i])); }
return res;
}
vm calc(vl ns, vl ks) {
int Q = sz(ns);
int M = Max(ks);
vi freq(M + 1);
V<vp> dist(M + 1);
rep(i, Q) {
freq[ks[i]]++;
dist[ks[i]].emplace_back(ns[i], i);
}
vi frui = mkrui(freq);
using Mat = Matrix<fps, 2, 2>;
Mat I;
I[0][0] = I[1][1] = fps{1};
I[0][1] = I[1][0] = fps{};
// 葉木を構成
int last = M + 1;
auto new_idx = [&](int l, int r) {
if (l == r) return -1;
if (l + 1 == r) return l;
return last++;
};
vi lchd(2 * M + 1, -1);
vi mchd(2 * M + 1, -1);
vi rchd(2 * M + 1, -1);
V<fps> mod(2 * M + 1);
auto precalc = [&](auto rc, int l, int r, bool sep_left = false,
bool sep_s = true) -> int {
int idx = new_idx(l, r);
// trc(l, r, idx, sep_left, sep_s);
if (idx == -1) return -1;
assert(l < r);
if (l + 1 == r) {
assert(l == idx);
V<fps> fs;
each2(n, _, dist[idx]) fs.push_back(fps{-n, 1});
mod[idx] = Pi(fs);
return idx;
}
// [l, m), [m, r) に分ける
int m = -1;
if (l + 2 == r or sep_left) {
mchd[idx] = m = l + 1;
lchd[idx] = rc(rc, l, m, false, true);
rchd[idx] = rc(rc, m, r, false, true);
} else if (sep_s) {
mchd[idx] = m = (l + r) / 2;
lchd[idx] = rc(rc, l, m, false, false);
rchd[idx] = rc(rc, m, r, false, false);
} else {
// [l, m) が 過半数を超えない最小の m
int ok = l + 1, ng = r, fsum = frui[r] - frui[l];
while (ok + 1 < ng) {
int med = (ok + ng) / 2;
((frui[med] - frui[l]) * 2 < fsum ? ok : ng) = med;
}
mchd[idx] = m = ok;
lchd[idx] = rc(rc, l, m, false, true);
rchd[idx] = rc(rc, m, r, true, true);
}
fps fl = ~idx ? mod[lchd[idx]] : fps{1};
fps fr = ~idx ? mod[rchd[idx]] : fps{1};
mod[idx] = fl * fr;
return idx;
};
int rootidx = precalc(precalc, 0, M + 1);
assert(last == 2 * M + 1);
trc("precalc ok");
vm ans(Q);
auto calc = [&](auto rc, int idx, int l, int r, const Mat &mat) -> Mat {
if (idx == -1) return I;
// trc(idx, l, r, mod[idx], mat);
Mat m2;
rep(i, 2) rep(j, 2) m2[i][j] = mat[i][j] % mod[idx];
// trc(idx, l, r, m2);
if (l + 1 == r) {
// trc(l, dist[idx]);
vm xs;
each2(n, _, dist[idx]) xs.push_back(n);
vm buf = FastMultiEval(m2[0][0], xs);
rep(i, sz(dist[idx])) {
mint g0 = mint{2}.pow(dist[idx][i].first);
ans[dist[idx][i].second] = g0 * buf[i];
}
Mat res;
mint a = l + 1;
res[0][0] = fps{(-a + 1) * 2, 2};
res[1][0] = fps{(-a + 2) * (a - 1) * C.inv(2), a - 1};
res[0][1] = fps{1};
return res;
}
int m = mchd[idx];
auto ml = rc(rc, lchd[idx], l, m, m2);
auto mr = rc(rc, rchd[idx], m, r, m2 * ml);
return ml * mr;
};
calc(calc, rootidx, 0, M + 1, I);
return ans;
}
vm calc2(vl ns, vl ks) {
int Q = sz(ns);
int M = Max(ks);
V<vp> dist(M + 1);
rep(i, Q) dist[ks[i]].emplace_back(ns[i], i);
using Mat = Matrix<fps, 2, 2>;
Mat I;
I[0][0] = I[1][1] = fps{1};
I[0][1] = I[1][0] = fps{};
int S = 1;
while (S < M + 1) S *= 2;
V<fps> mod(2 * S);
rep(i, M + 1) {
V<fps> v;
each2(n, _, dist[i]) v.push_back({-n, 1});
mod[S + i] = Pi(v);
}
reg(i, M + 1, S) mod[S + i] = {1};
for (int i = S - 1; i; i--) mod[i] = mod[i * 2] * mod[i * 2 + 1];
vm ans(Q);
auto calc = [&](auto rc, int idx, int l, int r, const Mat &mat) -> Mat {
if (M < l) return I;
if (l + 1 == r) {
vm xs;
each2(n, _, dist[l]) xs.push_back(n);
vm buf = FastMultiEval(mat[0][0] % mod[idx], xs);
rep(i, sz(dist[l])) {
mint g0 = mint{2}.pow(dist[l][i].first);
ans[dist[l][i].second] = g0 * buf[i];
}
Mat res;
mint a = l + 1;
res[0][0] = fps{(-a + 1) * 2, 2};
res[1][0] = fps{(-a + 2) * (a - 1) * C.inv(2), a - 1};
res[0][1] = fps{1};
return res;
}
Mat m2;
rep(i, 2) rep(j, 2) m2[i][j] = mat[i][j] % mod[idx];
auto ml = rc(rc, idx * 2 + 0, l, (l + r) / 2, m2);
auto mr = rc(rc, idx * 2 + 1, (l + r) / 2, r, m2 * ml);
return ml * mr;
};
calc(calc, 1, 0, S, I);
return ans;
}
void test2() {
vl ns, ks;
int Q = 100;
rep(_, Q) {
int N = rng(1, 100);
int K = rng(0, N);
ns.push_back(N);
ks.push_back(K);
}
trc(ns);
trc(ks);
auto ansn = naive3(ns, ks);
auto anss = calc(ns, ks);
if (ansn != anss) {
trc(ansn);
trc(anss);
exit(1);
}
trc2("OK");
}
void q() {
// test1();
// test2();
ini(Q);
vl ns(Q), ks(Q);
rep(i, Q) in(ns[i], ks[i]);
auto ans = calc2(ns, ks);
rep(i, Q) { out(ans[i] / (mint{2}.pow(ns[i]))); }
}
void Nyaan::solve() {
int T = 1;
// in(T);
while (T--) q();
}