結果
| 問題 |
No.2166 Paint and Fill
|
| コンテスト | |
| ユーザー |
 Nachia
|
| 提出日時 | 2022-12-17 02:04:00 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 3,008 ms / 10,000 ms |
| コード長 | 33,741 bytes |
| コンパイル時間 | 3,020 ms |
| コンパイル使用メモリ | 143,932 KB |
| 最終ジャッジ日時 | 2025-02-09 14:56:14 |
|
ジャッジサーバーID （参考情報） |
judge1 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 38 |
ソースコード
#line 2 "nachia\\fps\\formal-power-series-struct.hpp"
#include <vector>
#include <algorithm>
#include <string>
#include <cassert>
#include <iostream>
#line 3 "nachia\\math-modulo\\modulo-primitive-root.hpp"
#include <utility>
namespace nachia{
template<unsigned int MOD>
struct PrimitiveRoot{
static constexpr unsigned long long powm(unsigned long long a, unsigned long long i) {
unsigned long long res = 1, aa = a;
while(i){
if(i & 1) res = res * aa % MOD;
aa = aa * aa % MOD;
i /= 2;
}
return res;
}
static constexpr bool ExamineVal(unsigned int g){
unsigned int t = MOD - 1;
for(unsigned long long d=2; d*d<=t; d++) if(t % d == 0){
if(powm(g, (MOD - 1) / d) == 1) return false;
while(t % d == 0) t /= d;
}
if(t != 1) if(powm(g, (MOD - 1) / t) == 1) return false;
return true;
}
static constexpr unsigned int GetVal(){
for(unsigned int x=2; x<MOD; x++) if(ExamineVal(x)) return x;
return 0;
}
static const unsigned int val = GetVal();
};
}
#line 3 "nachia\\math\\combination.hpp"
namespace nachia{
template<class Modint>
class Comb{
private:
std::vector<Modint> F;
std::vector<Modint> iF;
public:
void extend(int newN){
int prevN = (int)F.size() - 1;
if(prevN >= newN) return;
F.resize(newN+1);
iF.resize(newN+1);
for(int i=prevN+1; i<=newN; i++) F[i] = F[i-1] * Modint::raw(i);
iF[newN] = F[newN].inv();
for(int i=newN; i>prevN; i--) iF[i-1] = iF[i] * Modint::raw(i);
}
Comb(int n = 1){
F.assign(2, Modint(1));
iF.assign(2, Modint(1));
extend(n);
}
Modint factorial(int n) const { return F[n]; }
Modint invFactorial(int n) const { return iF[n]; }
Modint invOf(int n) const { return iF[n] * F[n-1]; }
Modint comb(int n, int r) const {
if(n < 0 || n < r || r < 0) return Modint(0);
return F[n] * iF[r] * iF[n-r];
}
Modint invComb(int n, int r) const {
if(n < 0 || n < r || r < 0) return Modint(0);
return iF[n] * F[r] * F[n-r];
}
Modint perm(int n, int r) const {
if(n < 0 || n < r || r < 0) return Modint(0);
return F[n] * iF[n-r];
}
Modint invPerm(int n, int r) const {
if(n < 0 || n < r || r < 0) return Modint(0);
return iF[n] * F[n-r];
}
Modint operator()(int n, int r) const { return comb(n,r); }
};
} // namespace nachia
#line 1 "nachia\\fps\\ntt-acl.hpp"
#line 2 "nachia\\fps\\ntt-interface.hpp"
namespace nachia {
template<class mint>
struct NttInterface{
template<class Iter>
void Butterfly(Iter, int) const {}
template<class Iter>
void IButterfly(Iter, int) const {}
template<class Iter>
void BitReversal(Iter a, int N) const {
for(int i=0, j=0; j<N; j++){
if(i < j) std::swap(a[i], a[j]);
for(int k = N>>1; k > (i^=k); k>>=1);
}
}
};
} // namespace nachia
#line 1 "nachia\\misc\\bit-operations.hpp"
#line 4 "nachia\\misc\\bit-operations.hpp"
namespace nachia{
int Popcount(unsigned long long c) noexcept {
#ifdef __GNUC__
return __builtin_popcountll(c);
#else
c = (c & (~0ull/3)) + ((c >> 1) & (~0ull/3));
c = (c & (~0ull/5)) + ((c >> 2) & (~0ull/5));
c = (c & (~0ull/17)) + ((c >> 4) & (~0ull/17));
c = (c * (~0ull/257)) >> 56;
return c;
#endif
}
// please ensure x != 0
int MsbIndex(unsigned long long x) noexcept {
#ifdef __GNUC__
return 63 - __builtin_clzll(x);
#else
int res = 0;
for(int d=32; d>=0; d>>=1) if(x >> d){ res |= d; x >>= d; }
return res;
#endif
}
// please ensure x != 0
int LsbIndex(unsigned long long x) noexcept {
#ifdef __GNUC__
return __builtin_ctzll(x);
#else
return msb_idx(x & -x);
#endif
}
}
#line 5 "nachia\\fps\\ntt-acl.hpp"
#include <iterator>
#line 8 "nachia\\fps\\ntt-acl.hpp"
#include <array>
namespace nachia{
constexpr int bsf_constexpr(unsigned int n) {
int x = 0;
while (!(n & (1 << x))) x++;
return x;
}
template <class mint>
struct NttFromAcl : NttInterface<mint> {
using u32 = unsigned int;
using u64 = unsigned long long;
static int ceil_pow2(int n) {
int x = 0;
while ((1U << x) < (u32)(n)) x++;
return x;
}
struct fft_info {
static constexpr u32 g = nachia::PrimitiveRoot<mint::mod()>::val;
static constexpr int rank2 = bsf_constexpr(mint::mod()-1);
std::array<mint, rank2+1> root;
std::array<mint, rank2+1> iroot;
std::array<mint, std::max(0, rank2-1)> rate2;
std::array<mint, std::max(0, rank2-1)> irate2;
std::array<mint, std::max(0, rank2-2)> rate3;
std::array<mint, std::max(0, rank2-2)> irate3;
fft_info(){
root[rank2] = mint(g).pow((mint::mod() - 1) >> rank2);
iroot[rank2] = root[rank2].inv();
for(int i=rank2-1; i>=0; i--){
root[i] = root[i+1] * root[i+1];
iroot[i] = iroot[i+1] * iroot[i+1];
}
mint prod = 1, iprod = 1;
for(int i=0; i<=rank2-2; i++){
rate2[i] = root[i+2] * prod;
irate2[i] = iroot[i+2] * iprod;
prod *= iroot[i+2];
iprod *= root[i+2];
}
prod = 1; iprod = 1;
for(int i=0; i<=rank2-3; i++){
rate3[i] = root[i+3] * prod;
irate3[i] = iroot[i+3] * iprod;
prod *= iroot[i+3];
iprod *= root[i+3];
}
}
};
template<class RandomAccessIterator>
void Butterfly(RandomAccessIterator a, int n) const {
int h = ceil_pow2(n);
static const fft_info info;
int len = 0;
while(len < h){
if(h-len == 1){
int p = 1 << (h-len-1);
mint rot = 1;
for(int s=0; s<(1<<len); s++){
int offset = s << (h-len);
for(int i=0; i<p; i++){
auto l = a[i+offset];
auto r = a[i+offset+p] * rot;
a[i+offset] = l+r;
a[i+offset+p] = l-r;
}
if(s+1 != (1<<len)) rot *= info.rate2[LsbIndex(~(u32)(s))];
}
len++;
} else {
int p = 1 << (h-len-2);
mint rot = 1, imag = info.root[2];
for(int s=0; s<(1<<len); s++){
mint rot2 = rot * rot;
mint rot3 = rot2 * rot;
int offset = s << (h-len);
for(int i=0; i<p; i++){
auto mod2 = 1ULL * mint::mod() * mint::mod();
auto a0 = 1ULL * a[i+offset].val();
auto a1 = 1ULL * a[i+offset+p].val() * rot.val();
auto a2 = 1ULL * a[i+offset+2*p].val() * rot2.val();
auto a3 = 1ULL * a[i+offset+3*p].val() * rot3.val();
auto a1na3imag = 1ULL * mint(a1 + mod2 - a3).val() * imag.val();
auto na2 = mod2 - a2;
a[i+offset] = a0 + a2 + a1 + a3;
a[i+offset+1*p] = a0 + a2 + (2 * mod2 - (a1 + a3));
a[i+offset+2*p] = a0 + na2 + a1na3imag;
a[i+offset+3*p] = a0 + na2 + (mod2 - a1na3imag);
}
if(s+1 != (1<<len)) rot *= info.rate3[LsbIndex(~(u32)(s))];
}
len += 2;
}
}
}
template<class RandomAccessIterator>
void IButterfly(RandomAccessIterator a, int n) const {
int h = ceil_pow2(n);
static const fft_info info;
constexpr int MOD = mint::mod();
int len = h;
while(len){
if(len == 1){
int p = 1 << (h-len);
mint irot = 1;
for(int s=0; s<(1<<(len-1)); s++){
int offset = s << (h-len+1);
for(int i=0; i<p; i++){
auto l = a[i+offset];
auto r = a[i+offset+p];
a[i+offset] = l+r;
a[i+offset+p] = (u64)(MOD + l.val() - r.val()) * irot.val();
}
if(s+1 != (1<<(len-1))) irot *= info.irate2[LsbIndex(~(u32)(s))];
}
len--;
} else {
int p = 1 << (h-len);
mint irot = 1, iimag = info.iroot[2];
for(int s=0; s<(1<<(len-2)); s++){
mint irot2 = irot * irot;
mint irot3 = irot2 * irot;
int offset = s << (h-len+2);
for(int i=0; i<p; i++){
auto a0 = 1ULL * a[i+offset+0*p].val();
auto a1 = 1ULL * a[i+offset+1*p].val();
auto a2 = 1ULL * a[i+offset+2*p].val();
auto a3 = 1ULL * a[i+offset+3*p].val();
auto a2na3iimag = 1ULL * mint((MOD + a2 - a3) * iimag.val()).val();
a[i+offset] = a0 + a1 + a2 + a3;
a[i+offset+1*p] = (a0 + (MOD - a1) + a2na3iimag) * irot.val();
a[i+offset+2*p] = (a0 + a1 + (MOD - a2) + (MOD - a3)) * irot2.val();
a[i+offset+3*p] = (a0 + (MOD - a1) + (MOD - a2na3iimag)) * irot3.val();
}
if(s+1 != (1<<(len-2))) irot *= info.irate3[LsbIndex(~(u32)(s))];
}
len -= 2;
}
}
}
};
} // namespace nachia
#line 10 "nachia\\fps\\formal-power-series-struct.hpp"
namespace nachia {
template<class Elem, class NttInst = NttFromAcl<Elem>>
struct FormalPowerSeriesNTT {
public:
using MyType = FormalPowerSeriesNTT;
static constexpr unsigned int MOD = Elem::mod();
static const NttInst nttInst;
private:
using u32 = unsigned int;
static const u32 zeta = nachia::PrimitiveRoot<MOD>::GetVal();
static Elem ZeroElem() noexcept { return Elem(0); }
static Elem OneElem() noexcept { return Elem(1); }
static Comb<Elem> comb;
std::vector<Elem> a;
public:
unsigned int size() const noexcept { return a.size(); }
Elem& operator[](unsigned int x) noexcept { return a[x]; }
const Elem& operator[](unsigned int x) const noexcept { return a[x]; }
Elem get_coeff(unsigned int x) const{ return (x < size()) ? a[x] : ZeroElem(); }
static Comb<Elem>& GetComb() { return comb; }
MyType& removeLeadingZeros(){
unsigned int newsz = size();
while(newsz && a[newsz-1].val() == 0) newsz--;
a.resize(newsz);
if(a.capacity() / 4 > newsz) a.shrink_to_fit();
return *this;
}
FormalPowerSeriesNTT(){ a = { }; }
FormalPowerSeriesNTT(unsigned int new_size) : a(new_size, ZeroElem()) {}
FormalPowerSeriesNTT(std::vector<Elem>&& src) : a(std::move(src)) {}
FormalPowerSeriesNTT(const std::vector<Elem>& src) : a(src) {}
MyType& ntt() {
int N = 1; while (N < (int)size()) N *= 2;
a.resize(N, ZeroElem());
nttInst.Butterfly(a.begin(), N);
return *this;
}
MyType& intt() {
nttInst.IButterfly(a.begin(), a.size());
Elem invN = Elem(size()).inv();
for(u32 i=0; i<size(); i++) a[i] *= invN;
return *this;
}
// returns [ a[l], a[l+1], a[l+2], ... , a[r-1] ]
// a[i] = 0 ( i < 0 OR size() <= i )
MyType getSlice(int l, int r) const {
if(l >= r) return MyType();
MyType res(r - l);
for(int i=l; i<r; i++) res[i-l] = (0 <= i && i < (int)size()) ? a[i] : ZeroElem();
return res;
}
MyType clip(int srcPos = 0, int srcLen = -1, int destPos = 0, int destSize = -1) const {
int l = std::min((int)size(), srcPos);
int r = srcLen < 0 ? (int)size() : std::min((int)size(), l + srcLen);
if(destSize < 0) destSize = r - l + destPos;
int dr = std::min(r-l, destSize - destPos);
MyType res(destSize);
for(int i=0; i<dr; i++) res[destPos+i] = a[l+i];
return res;
}
// upper < 0 -> upper = lower
MyType& capSize(int lower, int upper = -1) {
if(upper < 0) upper = lower;
if(upper <= (int)size()) a.resize(upper);
if((int)size() <= lower) a.resize(lower, ZeroElem());
return *this;
}
MyType& mulEach(const MyType& other, size_t maxi = ~(size_t)0){
maxi = std::min(maxi, (size_t)std::min(size(), other.size()));
for(size_t i=0; i<maxi; i++) a[i] *= other[i];
return *this;
}
MyType& times(Elem x){
int n = size();
for(int i=0; i<n; i++) a[i] *= x;
return *this;
}
MyType& clrRange(int l, int r){
for(int i=l; i<r; i++) a[i] = 0;
return *this;
}
static MyType convolution(const MyType& a, const MyType& b, int sz = -1){
if(a.size() <= 30 || b.size() <= 30){
if(a.size() > 30) return convolution(b,a);
if(sz < 0) sz = std::max(0, (int)(a.size() + b.size()) - 1);
std::vector<Elem> res(sz);
for(u32 i=0; i<a.size(); i++) for(u32 j=0; j<b.size() && i+j<(u32)sz; j++) res[i+j] += a[i] * b[j];
return res;
}
int z = a.size() + b.size() - 1;
int Z = 1; while(Z < z) Z *= 2;
if(sz == -1) sz = z;
MyType ax = a.getSlice(0, Z);
MyType bx = b.getSlice(0, Z);
bx.ntt();
return ax.ntt().mulEach(bx).intt().clip(0, sz);
}
static MyType back_half_convolution(unsigned int sz, const MyType& smaller, const MyType& larger){
assert(smaller.size() <= sz);
assert(larger.size() <= sz*2);
if(sz <= 5) return convolution(smaller, larger).getSlice(sz, sz*2);
int z = sz*2;
int Z = 1; while(Z < z) Z *= 2;
MyType ax = smaller.getSlice(0, Z).ntt();
MyType bx = larger.getSlice(0, Z).ntt();
return ax.mulEach(bx).intt().getSlice(sz, sz*2);
}
// 1
// ----- = 1 + f + f^2 + f^3 + ...
// 1-f
MyType power_sum(unsigned int sz) const {
if (sz == 0) { return {}; }
int q = std::min((int)sz, 32);
MyType x = MyType(q);
x[0] = OneElem();
for(int i=1; i<q; i++) for(int j=1; j<=std::min(i,(int)a.size()-1); j++) x[i] += x[i-j] * a[j];
while(x.size() < sz){
u32 hN = x.size(), N = hN*2;
MyType a = x.clip(0, hN, 0, N);
MyType b = clip(0, N, 0, N);
a.ntt();
b.ntt().mulEach(a).intt().clrRange(0,hN).ntt().mulEach(a).intt();
for(u32 i=0; i<hN; i++) b[i] = x[i];
std::swap(b, x);
}
if(x.size() != sz) x = x.clip(0, sz);
return x;
}
MyType inv(unsigned int sz) const {
Elem iA0 = a[0].inv();
MyType xA = clip(0, std::min(sz, size()));
xA.times(-iA0);
xA[0] = 0;
xA = xA.power_sum(sz);
return xA.times(iA0);
}
MyType& difference(){
if(size() == 0) return *this;
for(u32 i=0; i+1<size(); i++) a[i] = a[i+1] * Elem::raw(i+1);
capSize(0, size() - 1);
return *this;
}
MyType& integral(){
if(size() == 0){
a.push_back(ZeroElem());
return *this;
}
capSize(size()+1);
comb.extend(size());
for(u32 i=size()-1; i>=1; i--) a[i] = a[i-1] * comb.invOf(i);
a[0] = ZeroElem();
return *this;
}
MyType copied() const { return MyType(*this); }
MyType log(unsigned int sz){
assert(sz != 0);
assert(a[0].val() == 1);
return convolution(inv(sz), copied().difference(), sz-1).integral();
}
MyType exp(unsigned int sz){
MyType res = MyType(std::vector<Elem>{ OneElem() });
while(res.size() < sz){
auto z = res.size();
auto tmp = res.log(z*2);
tmp[0] = -OneElem();
for(u32 i=0; i<z*2 && i<size(); i++) tmp[i] = a[i] - tmp[i];
tmp = back_half_convolution(z, res, tmp);
res.capSize(std::min(sz, z*2), z);
for(u32 i=z; i<res.size(); i++) res[i] = tmp[i-z];
}
return res;
}
MyType& reverse(){ std::reverse(a.begin(), a.end()); return *this; }
MyType pow(unsigned long long k){
int n = size();
if(k == 0){
auto res = MyType(n);
res[0] = 1;
return res;
}
int ctz = 0;
while(ctz<n && a[ctz].val() == 0) ctz++;
if((unsigned long long)ctz >= (n-1) / k + 1) return MyType(n);
MyType res = clip(ctz, n);
Elem a0 = res[0];
res.times(a0.inv());
res = res.log(n);
res.times(Elem(k));
res = res.exp(n);
res.times(a0.pow(k));
ctz *= k;
return res;
}
auto begin(){ return a.begin(); }
auto end(){ return a.end(); }
auto begin() const { return a.begin(); }
auto end() const { return a.end(); }
std::string to_string() const {
std::string res = "[";
for(auto x : a){ res += " "; res += std::to_string(x.val()); }
res += " ]";
return res;
}
std::vector<Elem> get_vector_moved(){
std::vector<Elem> res = std::move(a);
a.clear();
return res;
}
MyType ax_plus_b(Elem a, Elem b) const {
auto buf = MyType(size() + 1);
for(u32 i=0; i<size(); i++) buf[i] += this->a[i] * b;
for(u32 i=0; i<size(); i++) buf[i+1] += this->a[i] * a;
return buf;
}
MyType operator+(const MyType& r) const {
auto sz = std::max(this->size(), r.size());
MyType res(sz);
for(u32 i=0; i<this->size(); i++) res[i] += this->operator[](i);
for(u32 i=0; i<r.size(); i++) res[i] += r[i];
return res;
}
MyType operator-(const MyType& r) const {
auto sz = std::max(this->size(), r.size());
MyType res(sz);
for(u32 i=0; i<this->size(); i++) res[i] += this->operator[](i);
for(u32 i=0; i<r.size(); i++) res[i] -= r[i];
return res;
}
MyType operator*(const MyType& r) const {
auto res = convolution(*this, r);
return std::move(res.removeLeadingZeros());
}
MyType& operator*=(const MyType& r){ (*this) = (*this) * r; return *this; }
MyType& operator*=(Elem m){ for(size_t i=0; i<a.size(); i++) a[i] *= m; return *this; }
MyType operator*(Elem m) const { MyType b = *this; b *= m; return b; }
Elem eval(Elem x) const {
int z = size();
Elem res = 0;
for(int i=z-1; i>=0; i--) res = res * x + a[i];
return res;
}
};
template<class Elem, class NttInst> Comb<Elem> FormalPowerSeriesNTT<Elem, NttInst>::comb;
template<class Elem, class NttInst> const NttInst FormalPowerSeriesNTT<Elem, NttInst>::nttInst;
} // namespace nachia
#line 5 "nachia\\linear\\simple-matrix.hpp"
namespace nachia{
template<class Elem>
struct SimpleMatrix{
private:
int h;
int w;
std::vector<Elem> elems;
public:
SimpleMatrix(int new_h=0, int new_w=0){ h = new_h; w = new_w; elems.assign(h * w, 0); }
SimpleMatrix(SimpleMatrix const&) = default;
int numRow() const { return h; }
int numColumn() const { return w; }
int height() const { return numRow(); }
int width() const { return numColumn(); }
typename std::vector<Elem>::iterator operator[](int y){ return elems.begin() + (y*w); }
typename std::vector<Elem>::const_iterator operator[](int y) const { return elems.begin() + (y*w); }
static SimpleMatrix Identity(int idx, Elem One){ auto res = SimpleMatrix(idx, idx); for(int i=0; i<idx; i++) res[i][i] = One; return res; }
void swapColumns(int x1, int x2){
assert(0 <= x1 && x1 < numColumn());
assert(0 <= x2 && x2 < numColumn());
for(int y=0; y<numRow(); y++) std::swap((*this)[y][x1], (*this)[y][x2]);
}
void swapRows(int y1, int y2){
assert(0 <= y1 && y1 < numRow());
assert(0 <= y2 && y2 < numRow());
for(int x=0; x<numColumn(); x++) std::swap((*this)[y1][x], (*this)[y2][x]);
}
SimpleMatrix operator*(const SimpleMatrix& r) const {
assert(width() == r.height());
auto res = SimpleMatrix(h, r.w);
for(int i=0; i<h; i++) for(int j=0; j<w; j++) for(int k=0; k<r.w; k++) res[i][k] = res[i][k] + (*this)[i][j] * r[j][k];
return res;
}
SimpleMatrix pow(unsigned long long i){
auto a = *this;
auto res = Identity(height());
while(i){
if(i % 2 == 1) res = res * a;
a = a * a;
i /= 2;
}
return res;
}
};
} // namespace nachia
#line 4 "nachia\\fps\\p-recursive-matrix-product.hpp"
namespace nachia{
template<class Elem>
SimpleMatrix<Elem> PRecursiveMatrixProduct(
SimpleMatrix<FormalPowerSeriesNTT<Elem>> p,
unsigned long long idx
){
struct ShiftOfSamplingPointsOfPolynomialUpdate{
using Fps = FormalPowerSeriesNTT<Elem>;
int n;
int N2;
Fps iF, F, iFI, iFIntt1, iFntt;
std::vector<Fps> iFIntt2s;
ShiftOfSamplingPointsOfPolynomialUpdate(int n, std::vector<Elem> sh){
this->n = n;
N2 = 1; while(N2 < n*2) N2 *= 2;
iF = Fps(n);
F = Fps(n);
F[0] = 1;
for(int i=1; i<n; i++) F[i] = F[i-1] * Elem::raw(i);
iF[n-1] = F[n-1].inv();
for(int i=n-1; i>=1; i--) iF[i-1] = iF[i] * Elem::raw(i);
iFI = Fps(n);
for(int i=0; i<n; i++) iFI[i] = (i%2) ? -iF[i] : iF[i];
iFIntt1 = iFI.clip(0, n, 0, N2); iFIntt1.ntt();
iFntt = iF.clip(0, n, 0, N2); iFntt.ntt();
for(size_t shi=0; shi<sh.size(); shi++){
Elem q = 1;
Fps T(N2); T[0] = Elem(1);
for(int i=1; i<n; i++) T[i] = iF[i] * (q *= (sh[shi] - Elem::raw(i-1)));
T.ntt();
iFIntt2s.push_back(std::move(T));
}
}
std::vector<std::vector<Elem>> calc(const std::vector<Elem>& points){
Fps P(N2);
for(int i=0; i<n; i++) P[i] = points[i] * iF[i];
P.ntt().mulEach(iFIntt1).intt().clrRange(n, N2).mulEach(F, n).reverse().ntt();
std::vector<std::vector<Elem>> res2(iFIntt2s.size());
for(size_t shi=0; shi<iFIntt2s.size(); shi++){
res2[shi] = P.clip().mulEach(iFIntt2s[shi]).intt().reverse().clrRange(n, N2).mulEach(iF, n).ntt().mulEach(iFntt).intt().mulEach(F, n).clip(0, n).get_vector_moved();
}
return res2;
}
};
using u64 = unsigned long long;
int h = p.height();
std::vector<std::vector<Elem>> res;
res.resize(h*h);
for(auto& a : res) a.resize(h);
u64 a = 1, b = 1;
for(int i=0; i<h; i++) for(int j=0; j<h; j++) while(b < p[i][j].size()) b <<= 1;
u64 maxA = 1, maxB = b;
while(maxA * maxB <= idx){ maxB <<= 1; maxA <<= 1; }
for(int i=0; i<h; i++) for(int j=0; j<h; j++){
res[i*h+j].resize(b);
for(u64 k=0; k<b; k++) res[i*h+j][k] = p[i][j].eval(Elem(maxA) * Elem(k));
}
auto EvalP = [p, h](Elem val) -> SimpleMatrix<Elem> {
SimpleMatrix<Elem> res(h, h);
for(int y=0; y<h; y++) for(int x=0; x<h; x++) res[y][x] = p[y][x].eval(val);
return res;
};
auto EvalL = [&res, h](u64 idx) -> SimpleMatrix<Elem> {
SimpleMatrix<Elem> g(h, h);
for(int y=0; y<h; y++) for(int x=0; x<h; x++) g[y][x] = res[y*h+x][idx];
return g;
};
while(b < maxB){
std::vector<Elem> sh(3);
sh[0] = Elem(b);
sh[1] = Elem(a) / Elem(maxA);
sh[2] = sh[0] + sh[1];
std::vector<std::vector<std::vector<Elem>>> shbuf(h*h);
auto shman = ShiftOfSamplingPointsOfPolynomialUpdate(b, sh);
for(int i=0; i<h*h; i++) shbuf[i] = shman.calc(res[i]);
std::vector<std::vector<Elem>> resbuf;
resbuf.assign(h*h, std::vector<Elem>(b*2));
for(int i=0; i<h; i++) for(int j=0; j<h; j++) for(int k=0; k<h; k++){
auto Lbeg1 = shbuf[i*h+j][1].begin();
auto Rbeg1 = res[j*h+k].begin();
auto destbeg1 = resbuf[i*h+k].begin();
for(u64 id=0; id<b; id++) destbeg1[id] += Lbeg1[id] * Rbeg1[id];
auto Lbeg2 = shbuf[i*h+j][2].begin();
auto Rbeg2 = shbuf[j*h+k][0].begin();
auto destbeg2 = resbuf[i*h+k].begin() + b;
for(u64 id=0; id<b; id++) destbeg2[id] += Lbeg2[id] * Rbeg2[id];
}
std::swap(res, resbuf);
a *= 2;
b *= 2;
}
u64 pos = 0;
SimpleMatrix<Elem> ans = SimpleMatrix<Elem>::Identity(h, Elem::raw(1));
while(pos + maxA <= idx){ ans = EvalL(pos / maxA) * ans; pos += maxA; }
while(pos < idx){ ans = EvalP(pos++) * ans; }
return ans;
}
} // namespace nachia
#line 2 "nachia\\misc\\fastio.hpp"
#include <cstdio>
#include <cctype>
#include <cstdint>
#line 6 "nachia\\misc\\fastio.hpp"
namespace nachia{
struct CInStream{
private:
static const unsigned int INPUT_BUF_SIZE = 1 << 17;
unsigned int p = INPUT_BUF_SIZE;
static char Q[INPUT_BUF_SIZE];
public:
using MyType = CInStream;
char seekChar(){
if(p == INPUT_BUF_SIZE){
size_t len = fread(Q, 1, INPUT_BUF_SIZE, stdin);
if(len != INPUT_BUF_SIZE) Q[len] = '\0';
p = 0;
}
return Q[p];
}
void skipSpace(){ while(isspace(seekChar())) p++; }
uint32_t nextU32(){
skipSpace();
uint32_t buf = 0;
while(true){
char tmp = seekChar();
if('9' < tmp || tmp < '0') break;
buf = buf * 10 + (tmp - '0');
p++;
}
return buf;
}
int32_t nextI32(){
skipSpace();
if(seekChar() == '-'){ p++; return (int32_t)(-nextU32()); }
return (int32_t)nextU32();
}
uint64_t nextU64(){
skipSpace();
uint64_t buf = 0;
while(true){
char tmp = seekChar();
if('9' < tmp || tmp < '0') break;
buf = buf * 10 + (tmp - '0');
p++;
}
return buf;
}
int64_t nextI64(){
skipSpace();
if(seekChar() == '-'){ p++; return (int64_t)(-nextU64()); }
return (int64_t)nextU64();
}
char nextChar(){ skipSpace(); char buf = seekChar(); p++; return buf; }
std::string nextToken(){
skipSpace();
std::string buf;
while(true){
char ch = seekChar();
if(isspace(ch) || ch == '\0') break;
buf.push_back(ch);
p++;
}
return buf;
}
MyType& operator>>(unsigned int& dest){ dest = nextU32(); return *this; }
MyType& operator>>(int& dest){ dest = nextI32(); return *this; }
MyType& operator>>(unsigned long& dest){ dest = nextU64(); return *this; }
MyType& operator>>(long& dest){ dest = nextI64(); return *this; }
MyType& operator>>(unsigned long long& dest){ dest = nextU64(); return *this; }
MyType& operator>>(long long& dest){ dest = nextI64(); return *this; }
MyType& operator>>(std::string& dest){ dest = nextToken(); return *this; }
MyType& operator>>(char& dest){ dest = nextChar(); return *this; }
} cin;
struct FastOutputTable{
char LZ[1000][4] = {};
char NLZ[1000][4] = {};
constexpr FastOutputTable(){
using u32 = uint_fast32_t;
for(u32 d=0; d<1000; d++){
LZ[d][0] = ('0' + d / 100 % 10);
LZ[d][1] = ('0' + d / 10 % 10);
LZ[d][2] = ('0' + d / 1 % 10);
LZ[d][3] = '\0';
}
for(u32 d=0; d<1000; d++){
u32 i = 0;
if(d >= 100) NLZ[d][i++] = ('0' + d / 100 % 10);
if(d >= 10) NLZ[d][i++] = ('0' + d / 10 % 10);
if(d >= 1) NLZ[d][i++] = ('0' + d / 1 % 10);
NLZ[d][i++] = '\0';
}
}
};
struct COutStream{
private:
using u32 = uint32_t;
using u64 = uint64_t;
using MyType = COutStream;
static const u32 OUTPUT_BUF_SIZE = 1 << 17;
static char Q[OUTPUT_BUF_SIZE];
static constexpr FastOutputTable TB = FastOutputTable();
u32 p = 0;
static constexpr u32 P10(u32 d){ return d ? P10(d-1)*10 : 1; }
static constexpr u64 P10L(u32 d){ return d ? P10L(d-1)*10 : 1; }
template<class T, class U> static void Fil(T& m, U& l, U x) noexcept { m = l/x; l -= m*x; }
void next_dig9(u32 x){
u32 y;
Fil(y, x, P10(6));
nextCstr(TB.LZ[y]);
Fil(y, x, P10(3));
nextCstr(TB.LZ[y]); nextCstr(TB.LZ[x]);
}
public:
void nextChar(char c){
Q[p++] = c;
if(p == OUTPUT_BUF_SIZE){ fwrite(Q, p, 1, stdout); p = 0; }
}
void nextEoln(){ nextChar('\n'); }
void nextCstr(const char* s){ while(*s) nextChar(*(s++)); }
void nextU32(uint32_t x){
u32 y = 0;
if(x >= P10(9)){
Fil(y, x, P10(9));
nextCstr(TB.NLZ[y]); next_dig9(x);
}
else if(x >= P10(6)){
Fil(y, x, P10(6));
nextCstr(TB.NLZ[y]);
Fil(y, x, P10(3));
nextCstr(TB.LZ[y]); nextCstr(TB.LZ[x]);
}
else if(x >= P10(3)){
Fil(y, x, P10(3));
nextCstr(TB.NLZ[y]); nextCstr(TB.LZ[x]);
}
else if(x >= 1) nextCstr(TB.NLZ[x]);
else nextChar('0');
}
void nextI32(int32_t x){
if(x >= 0) nextU32(x);
else{ nextChar('-'); nextU32((u32)-x); }
}
void nextU64(uint64_t x){
u32 y = 0;
if(x >= P10L(18)){
Fil(y, x, P10L(18));
nextU32(y);
Fil(y, x, P10L(9));
next_dig9(y); next_dig9(x);
}
else if(x >= P10L(9)){
Fil(y, x, P10L(9));
nextU32(y); next_dig9(x);
}
else nextU32(x);
}
void nextI64(int64_t x){
if(x >= 0) nextU64(x);
else{ nextChar('-'); nextU64((u64)-x); }
}
void writeToFile(bool flush = false){
fwrite(Q, p, 1, stdout);
if(flush) fflush(stdout);
p = 0;
}
COutStream(){ Q[0] = 0; }
~COutStream(){ writeToFile(); }
MyType& operator<<(unsigned int tg){ nextU32(tg); return *this; }
MyType& operator<<(unsigned long tg){ nextU64(tg); return *this; }
MyType& operator<<(unsigned long long tg){ nextU64(tg); return *this; }
MyType& operator<<(int tg){ nextI32(tg); return *this; }
MyType& operator<<(long tg){ nextI64(tg); return *this; }
MyType& operator<<(long long tg){ nextI64(tg); return *this; }
MyType& operator<<(const std::string& tg){ nextCstr(tg.c_str()); return *this; }
MyType& operator<<(const char* tg){ nextCstr(tg); return *this; }
MyType& operator<<(char tg){ nextChar(tg); return *this; }
} cout;
char CInStream::Q[INPUT_BUF_SIZE];
char COutStream::Q[OUTPUT_BUF_SIZE];
} // namespace nachia
#line 3 "Main.cpp"
#include <atcoder/modint>
int main(){
using Modint = atcoder::static_modint<998244353>;
using Polynomial = nachia::FormalPowerSeriesNTT<Modint>;
using PolynomialMat = nachia::SimpleMatrix<Polynomial>;
using nachia::cin, nachia::cout;
auto MatMod = [&](const PolynomialMat& mat, const Polynomial& mod) -> PolynomialMat {
int n = mat.height();
PolynomialMat res(n, n);
int maxlen = 0;
for(int i=0; i<n; i++) for(int j=0; j<n; j++) maxlen = std::max(maxlen, (int)mat[i][j].size());
int deg = mod.size();
if(maxlen < deg) return mat;
auto K = mod;
K = K.reverse().inv(maxlen - deg + 1);
for(int i=0; i<n; i++) for(int j=0; j<n; j++){
auto buf = mat[i][j];
if(buf.size() < mod.size()){ res[i][j] = std::move(buf); continue; }
auto div = buf.clip(deg-1);
int divlen = div.size();
div.reverse(); div = (div * K.clip(0, divlen)).clip(0, divlen);
div.reverse();
res[i][j] = (mat[i][j] - div * mod).clip(0, deg-1);
}
return res;
};
int T; cin >> T;
if(T <= 5){
for(int t=0; t<T; t++){
unsigned long long N, K; cin >> N >> K;
if(K >= 998244353){ cout << "0\n"; continue; }
PolynomialMat M_nX = PolynomialMat(2,2);
M_nX[0][0] = std::vector<Modint>{ Modint(N) * 2 , -Modint(2) }; // 2N - 2k
M_nX[0][1] = std::vector<Modint>{ 0, (Modint(N)*2+1) / 2, -Modint(1) / 2 }; // (2N+1)k/2 - k^2/2
M_nX[1][0] = std::vector<Modint>{ 1 };
M_nX[1][1] = std::vector<Modint>{};
auto ansMat = nachia::PRecursiveMatrixProduct(M_nX, K);
Modint ans = ansMat[0][0];
cout << ans.val() << '\n';
}
}
else{
int MAX_K = 100000;
int MATRIX_QUERY = 1001001001;
std::vector<std::pair<unsigned long long, int>> NK(T);
for(auto& nk : NK) cin >> nk.first >> nk.second;
std::vector<std::pair<int, int>> queries;
for(int k=0; k<MAX_K; k++) queries.emplace_back(k, MATRIX_QUERY);
for(int t=0; t<T; t++) queries.emplace_back(NK[t].second, t);
std::sort(queries.begin(), queries.end());
int segN = 1;
while(segN < (int)queries.size()) segN *= 2;
std::vector<PolynomialMat> FX;
std::vector<Polynomial> KX;
FX.assign(segN*2, PolynomialMat::Identity(2, Polynomial(std::vector<Modint>{1})));
KX.assign(segN*2, Polynomial(std::vector<Modint>{1}));
for(int q=0; q<(int)queries.size(); q++){
if(queries[q].second == MATRIX_QUERY){
int k = queries[q].first;
FX[segN+q][0][0] = std::vector<Modint>{ -Modint(k)*2, Modint(2) }; // 2N - 2k
FX[segN+q][0][1] = std::vector<Modint>{ Modint(k)*(1-k) / 2, Modint(k) }; // Nk + k(1-k)/2
FX[segN+q][1][0] = std::vector<Modint>{ 1 };
FX[segN+q][1][1] = std::vector<Modint>{};
}
else{
unsigned long long N = NK[queries[q].second].first;
KX[segN+q] = Polynomial(std::vector<Modint>{ -Modint(N), 1 }); // x - N
}
}
for(int i=segN-1; i>=1; i--) FX[i] = FX[i*2+1] * FX[i*2];
for(int i=segN-1; i>=1; i--) KX[i] = KX[i*2+1] * KX[i*2];
std::vector<PolynomialMat> FXmodKX(segN*2);
FXmodKX[1] = MatMod(PolynomialMat::Identity(2, Polynomial(std::vector<Modint>{1})), KX[1]);
for(int i=1; i<=segN-1; i++){
FXmodKX[i*2] = MatMod(FXmodKX[i], KX[i*2]);
FXmodKX[i*2+1] = MatMod(FX[i*2] * FXmodKX[i], KX[i*2+1]);
}
std::vector<Modint> ans(T);
for(int q=0; q<(int)queries.size(); q++){
if(queries[q].second != MATRIX_QUERY){
ans[queries[q].second] = FXmodKX[segN+q][0][0].eval(0);
}
}
for(int i=0; i<T; i++) cout << ans[i].val() << '\n';
}
return 0;
}