結果
| 問題 | No.2166 Paint and Fill |
| ユーザー |
 tko919
|
| 提出日時 | 2022-12-23 22:45:05 |
| 言語 | C++17 (gcc 13.2.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 6,739 ms / 10,000 ms |
| コード長 | 26,188 bytes |
| コンパイル時間 | 6,290 ms |
| コンパイル使用メモリ | 280,092 KB |
| 実行使用メモリ | 255,660 KB |
| 最終ジャッジ日時 | 2023-08-11 12:10:06 |
| 合計ジャッジ時間 | 170,557 ms |
|
ジャッジサーバーID （参考情報） |
judge15 / judge12 |
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 | 2,659 ms
209,968 KB |
| testcase_01 | AC | 799 ms
31,312 KB |
| testcase_02 | AC | 3,507 ms
223,440 KB |
| testcase_03 | AC | 2,679 ms
210,416 KB |
| testcase_04 | AC | 2,688 ms
210,516 KB |
| testcase_05 | AC | 2,683 ms
210,324 KB |
| testcase_06 | AC | 2,684 ms
210,400 KB |
| testcase_07 | AC | 2,683 ms
210,388 KB |
| testcase_08 | AC | 3,614 ms
214,780 KB |
| testcase_09 | AC | 3,594 ms
214,652 KB |
| testcase_10 | AC | 3,590 ms
214,668 KB |
| testcase_11 | AC | 3,610 ms
214,888 KB |
| testcase_12 | AC | 3,608 ms
214,640 KB |
| testcase_13 | AC | 6,184 ms
255,528 KB |
| testcase_14 | AC | 6,362 ms
255,660 KB |
| testcase_15 | AC | 6,252 ms
255,556 KB |
| testcase_16 | AC | 6,171 ms
255,368 KB |
| testcase_17 | AC | 6,160 ms
255,328 KB |
| testcase_18 | AC | 6,082 ms
245,924 KB |
| testcase_19 | AC | 5,947 ms
245,948 KB |
| testcase_20 | AC | 6,739 ms
245,928 KB |
| testcase_21 | AC | 6,516 ms
243,120 KB |
| testcase_22 | AC | 6,649 ms
250,100 KB |
| testcase_23 | AC | 5,444 ms
238,512 KB |
| testcase_24 | AC | 5,294 ms
237,528 KB |
| testcase_25 | AC | 2 ms
4,380 KB |
| testcase_26 | AC | 2 ms
4,380 KB |
| testcase_27 | AC | 2,409 ms
31,608 KB |
| testcase_28 | AC | 3,015 ms
31,196 KB |
| testcase_29 | AC | 2,475 ms
31,592 KB |
| testcase_30 | AC | 3,704 ms
31,552 KB |
| testcase_31 | AC | 3,731 ms
31,640 KB |
| testcase_32 | AC | 3,730 ms
31,576 KB |
| testcase_33 | AC | 3,737 ms
31,548 KB |
| testcase_34 | AC | 3,731 ms
31,544 KB |
| testcase_35 | AC | 3,759 ms
31,824 KB |
| testcase_36 | AC | 3,755 ms
31,624 KB |
| testcase_37 | AC | 3,759 ms
31,592 KB |
| testcase_38 | AC | 3,757 ms
31,544 KB |
| testcase_39 | AC | 3,754 ms
31,768 KB |
ソースコード
#line 1 "library/Template/template.hpp"
#include <bits/stdc++.h>
using namespace std;
#define rep(i,a,b) for(int i=(int)(a);i<(int)(b);i++)
#define ALL(v) (v).begin(),(v).end()
using ll=long long int;
const int inf = 0x3fffffff;
const ll INF = 0x1fffffffffffffff;
template<typename T>inline bool chmax(T& a,T b){if(a<b){a=b;return 1;}return 0;}
template<typename T>inline bool chmin(T& a,T b){if(a>b){a=b;return 1;}return 0;}
#line 2 "library/Utility/fastio.hpp"
#include <unistd.h>
class FastIO{
static constexpr int L=1<<16;
char rdbuf[L];
int rdLeft=0,rdRight=0;
inline void reload(){
int len=rdRight-rdLeft;
memmove(rdbuf,rdbuf+rdLeft,len);
rdLeft=0,rdRight=len;
rdRight+=fread(rdbuf+len,1,L-len,stdin);
}
inline bool skip(){
for(;;){
while(rdLeft!=rdRight and rdbuf[rdLeft]<=' ')rdLeft++;
if(rdLeft==rdRight){
reload();
if(rdLeft==rdRight)return false;
}
else break;
}
return true;
}
template<typename T,enable_if_t<is_integral<T>::value,int> =0>inline bool _read(T& x){
if(!skip())return false;
if(rdLeft+20>=rdRight)reload();
bool neg=false;
if(rdbuf[rdLeft]=='-'){
neg=true;
rdLeft++;
}
x=0;
while(rdbuf[rdLeft]>='0' and rdLeft<rdRight){
x=x*10+(neg?-(rdbuf[rdLeft++]^48):(rdbuf[rdLeft++]^48));
}
return true;
}
template<typename T,enable_if_t<is_floating_point<T>::value,int> =0>inline bool _read(T& x){
if(!skip())return false;
if(rdLeft+20>=rdRight)reload();
bool neg=false;
if(rdbuf[rdLeft]=='-'){
neg=true;
rdLeft++;
}
x=0;
while(rdbuf[rdLeft]>='0' and rdbuf[rdLeft]<='9' and rdLeft<rdRight){
x=x*10+(rdbuf[rdLeft++]^48);
}
if(rdbuf[rdLeft]!='.')return true;
rdLeft++;
T base=.1;
while(rdbuf[rdLeft]>='0' and rdbuf[rdLeft]<='9' and rdLeft<rdRight){
x+=base*(rdbuf[rdLeft++]^48);
base*=.1;
}
if(neg)x=-x;
return true;
}
inline bool _read(char& x){
if(!skip())return false;
if(rdLeft+1>=rdRight)reload();
x=rdbuf[rdLeft++];
return true;
}
inline bool _read(string& x){
if(!skip())return false;
for(;;){
int pos=rdLeft;
while(pos<rdRight and rdbuf[pos]>' ')pos++;
x.append(rdbuf+rdLeft,pos-rdLeft);
if(rdLeft==pos)break;
rdLeft=pos;
if(rdLeft==rdRight)reload();
else break;
}
return true;
}
template<typename T>inline bool _read(vector<T>& v){
for(auto& x:v){
if(!_read(x))return false;
}
return true;
}
char wtbuf[L],tmp[50];
int wtRight=0;
inline void flush(){
fwrite(wtbuf,1,wtRight,stdout);
wtRight=0;
}
inline void _write(const char& x){
if(wtRight>L-32)flush();
wtbuf[wtRight++]=x;
}
inline void _write(const string& x){
for(auto& c:x)_write(c);
}
template<typename T,enable_if_t<is_integral<T>::value,int> =0>inline void _write(T x){
if(wtRight>L-32)flush();
if(x==0){
_write('0');
return;
}
else if(x<0){
_write('-');
if (__builtin_expect(x == std::numeric_limits<T>::min(), 0)) {
switch (sizeof(x)) {
case 2: _write("32768"); return;
case 4: _write("2147483648"); return;
case 8: _write("9223372036854775808"); return;
}
}
x=-x;
}
int pos=0;
while(x!=0){
tmp[pos++]=char((x%10)|48);
x/=10;
}
rep(i,0,pos)wtbuf[wtRight+i]=tmp[pos-1-i];
wtRight+=pos;
}
template<typename T>inline void _write(const vector<T>& v){
rep(i,0,v.size()){
if(i)_write(' ');
_write(v[i]);
}
}
public:
FastIO(){}
~FastIO(){flush();}
inline void read(){}
template <typename Head, typename... Tail>inline void read(Head& head,Tail&... tail){
assert(_read(head));
read(tail...);
}
template<bool ln=true,bool space=false>inline void write(){if(ln)_write('\n');}
template <bool ln=true,bool space=false,typename Head, typename... Tail>inline void write(const Head& head,const Tail&... tail){
if(space)_write(' ');
_write(head);
write<ln,true>(tail...);
}
};
/**
* @brief Fast IO
*/
#line 3 "sol.cpp"
#line 2 "library/Math/modint.hpp"
template<int mod=1000000007>struct fp {
int v; static int get_mod(){return mod;}
int inv() const{
int tmp,a=v,b=mod,x=1,y=0;
while(b)tmp=a/b,a-=tmp*b,swap(a,b),x-=tmp*y,swap(x,y);
if(x<0){x+=mod;} return x;
}
fp(ll x=0){init(x%mod+mod);}
fp& init(ll x){v=(x<mod?x:x-mod); return *this;}
fp operator-()const{return fp()-*this;}
fp pow(ll t){assert(t>=0); fp res=1,b=*this; while(t){if(t&1)res*=b;b*=b;t>>=1;} return res;}
fp& operator+=(const fp& x){return init(v+x.v);}
fp& operator-=(const fp& x){return init(v+mod-x.v);}
fp& operator*=(const fp& x){v=ll(v)*x.v%mod; return *this;}
fp& operator/=(const fp& x){v=ll(v)*x.inv()%mod; return *this;}
fp operator+(const fp& x)const{return fp(*this)+=x;}
fp operator-(const fp& x)const{return fp(*this)-=x;}
fp operator*(const fp& x)const{return fp(*this)*=x;}
fp operator/(const fp& x)const{return fp(*this)/=x;}
bool operator==(const fp& x)const{return v==x.v;}
bool operator!=(const fp& x)const{return v!=x.v;}
friend istream& operator>>(istream& is,fp& x){return is>>x.v;}
friend ostream& operator<<(ostream& os,const fp& x){return os<<x.v;}
};
template<typename T>struct factorial {
vector<T> Fact,Finv,Inv;
factorial(int maxx){
Fact.resize(maxx); Finv.resize(maxx); Inv.resize(maxx);
Fact[0]=Fact[1]=Finv[0]=Finv[1]=Inv[1]=1;
rep(i,2,maxx){Fact[i]=Fact[i-1]*i;} Finv[maxx-1]=Fact[maxx-1].inv();
for(int i=maxx-1;i>=2;i--){Finv[i-1]=Finv[i]*i; Inv[i]=Finv[i]*Fact[i-1];}
}
T fact(int n,bool inv=0){if(n<0)return 0; return (inv?Finv[n]:Fact[n]);}
T inv(int n){if(n<0)return 0; return Inv[n];}
T nPr(int n,int r,bool inv=0){if(n<0||n<r||r<0)return 0; return fact(n,inv)*fact(n-r,inv^1);}
T nCr(int n,int r,bool inv=0){if(n<0||n<r||r<0)return 0; return fact(n,inv)*fact(r,inv^1)*fact(n-r,inv^1);}
T nHr(int n,int r,bool inv=0){return nCr(n+r-1,r,inv);}
};
/**
* @brief Modint
*/
#line 2 "library/Convolution/ntt.hpp"
template<typename T,unsigned p=3>struct NTT{
vector<T> rt,irt;
NTT(int lg=21){
unsigned m=T::get_mod()-1; T prt=p;
rt.resize(lg); irt.resize(lg);
rep(k,0,lg){
rt[k]=-prt.pow(m>>(k+2));
irt[k]=rt[k].inv();
}
}
void ntt(vector<T>& f,bool inv=0){
int n=f.size();
if(inv){
for(int m=1;m<n;m<<=1){ T w=1;
for(int s=0,t=0;s<n;s+=m*2){
for(int i=s,j=s+m;i<s+m;i++,j++){
auto x=f[i],y=f[j];
f[i]=x+y; f[j]=(x-y)*w;
} w*=irt[__builtin_ctz(++t)];
}
} T mul=T(n).inv(); rep(i,0,n)f[i]*=mul;
}else{
for(int m=n;m>>=1;){ T w=1;
for(int s=0,t=0;s<n;s+=m*2){
for(int i=s,j=s+m;i<s+m;i++,j++){
auto x=f[i],y=f[j]*w;
f[i]=x+y; f[j]=x-y;
} w*=rt[__builtin_ctz(++t)];
}
}
}
}
vector<T> mult(const vector<T>& a,const vector<T>& b,bool same=0){
if(a.empty() or b.empty())return vector<T>();
int n=a.size()+b.size()-1,m=1<<__lg(n*2-1);
vector<T> res(m); rep(i,0,a.size()){res[i]=a[i];} ntt(res);
if(same)rep(i,0,m)res[i]*=res[i];
else{
vector<T> c(m); rep(i,0,b.size())c[i]=b[i];
ntt(c); rep(i,0,m)res[i]*=c[i];
} ntt(res,1); res.resize(n); return res;
}
};
/**
* @brief Number Theoretic Transform
*/
#line 2 "library/FPS/fps.hpp"
template<typename T>struct Poly:vector<T>{
Poly(int n=0){this->assign(n,T());}
Poly(const vector<T>& f){this->assign(ALL(f));}
T eval(const T& x){
T res;
for(int i=this->size()-1;i>=0;i--)res*=x,res+=this->at(i);
return res;
}
Poly rev()const{Poly res=*this; reverse(ALL(res)); return res;}
void shrink(){while(!this->empty() and this->back()==0)this->pop_back();}
vector<T> mult(const vector<T>& a,const vector<T>& b,bool same=0)const{
if(a.empty() or b.empty())return vector<T>();
int n=a.size()+b.size()-1,m=1<<__lg(n*2-1);
vector<T> res(m);
rep(i,0,a.size())res[i]=a[i];
NTT(res,0);
if(same)rep(i,0,m)res[i]*=res[i];
else{
vector<T> c(m);
rep(i,0,b.size())c[i]=b[i];
NTT(c,0);
rep(i,0,m)res[i]*=c[i];
}
NTT(res,1);
res.resize(n);
return res;
}
Poly square()const{return Poly(mult(*this,*this,1));}
Poly operator-()const{return Poly()-*this;}
Poly operator+(const Poly& g)const{return Poly(*this)+=g;}
Poly operator+(const T& g)const{return Poly(*this)+=g;}
Poly operator-(const Poly& g)const{return Poly(*this)-=g;}
Poly operator-(const T& g)const{return Poly(*this)-=g;}
Poly operator*(const Poly& g)const{return Poly(*this)*=g;}
Poly operator*(const T& g)const{return Poly(*this)*=g;}
Poly operator/(const Poly& g)const{return Poly(*this)/=g;}
Poly operator%(const Poly& g)const{return Poly(*this)%=g;}
Poly& operator+=(const Poly& g){
if(g.size()>this->size())this->resize(g.size());
rep(i,0,g.size()){(*this)[i]+=g[i];} return *this;
}
Poly& operator+=(const T& g){
if(this->empty())this->push_back(0);
(*this)[0]+=g; return *this;
}
Poly& operator-=(const Poly& g){
if(g.size()>this->size())this->resize(g.size());
rep(i,0,g.size()){(*this)[i]-=g[i];} return *this;
}
Poly& operator-=(const T& g){
if(this->empty())this->push_back(0);
(*this)[0]-=g; return *this;
}
Poly& operator*=(const Poly& g){
*this=mult(*this,g,0);
return *this;
}
Poly& operator*=(const T& g){
rep(i,0,this->size())(*this)[i]*=g;
return *this;
}
Poly& operator/=(const Poly& g){
if(g.size()>this->size()){
this->clear(); return *this;
}
Poly g2=g;
reverse(ALL(*this));
reverse(ALL(g2));
int n=this->size()-g2.size()+1;
this->resize(n); g2.resize(n);
*this*=g2.inv(); this->resize(n);
reverse(ALL(*this));
shrink();
return *this;
}
Poly& operator%=(const Poly& g){*this-=*this/g*g; shrink(); return *this;}
Poly diff()const{
Poly res(this->size()-1);
rep(i,0,res.size())res[i]=(*this)[i+1]*(i+1);
return res;
}
Poly inte()const{
Poly res(this->size()+1);
for(int i=res.size()-1;i;i--)res[i]=(*this)[i-1]/i;
return res;
}
Poly log()const{
assert(this->front()==1); const int n=this->size();
Poly res=diff()*inv(); res=res.inte();
res.resize(n); return res;
}
Poly shift(const int& c)const{
const int n=this->size();
Poly res=*this,g(n); g[0]=1; rep(i,1,n)g[i]=g[i-1]*c/i;
vector<T> fact(n,1);
rep(i,0,n){
if(i)fact[i]=fact[i-1]*i;
res[i]*=fact[i];
}
res=res.rev();
res*=g;
res.resize(n);
res=res.rev();
rep(i,0,n)res[i]/=fact[i];
return res;
}
Poly inv()const{
const int n=this->size();
Poly res(1); res.front()=T(1)/this->front();
for(int k=1;k<n;k<<=1){
Poly f(k*2),g(k*2);
rep(i,0,min(n,k*2))f[i]=(*this)[i];
rep(i,0,k)g[i]=res[i];
NTT(f,0);
NTT(g,0);
rep(i,0,k*2)f[i]*=g[i];
NTT(f,1);
rep(i,0,k){f[i]=0; f[i+k]=-f[i+k];}
NTT(f,0);
rep(i,0,k*2)f[i]*=g[i];
NTT(f,1);
rep(i,0,k)f[i]=res[i];
swap(res,f);
} res.resize(n); return res;
}
Poly exp()const{
const int n=this->size();
if(n==1)return Poly({T(1)});
Poly b(2),c(1),z1,z2(2);
b[0]=c[0]=z2[0]=z2[1]=1; b[1]=(*this)[1];
for(int k=2;k<n;k<<=1){
Poly y=b;
y.resize(k*2);
NTT(y,0);
z1=z2;
Poly z(k);
rep(i,0,k)z[i]=y[i]*z1[i];
NTT(z,1);
rep(i,0,k>>1)z[i]=0;
NTT(z,0);
rep(i,0,k)z[i]*=-z1[i];
NTT(z,1);
c.insert(c.end(),z.begin()+(k>>1),z.end());
z2=c;
z2.resize(k*2);
NTT(z2,0);
Poly x=*this;
x.resize(k);
x=x.diff();x.resize(k);
NTT(x,0);
rep(i,0,k)x[i]*=y[i];
NTT(x,1);
Poly bb=b.diff();
rep(i,0,k-1)x[i]-=bb[i];
x.resize(k*2);
rep(i,0,k-1){x[k+i]=x[i]; x[i]=0;}
NTT(x,0);
rep(i,0,k*2)x[i]*=z2[i];
NTT(x,1);
x.pop_back();
x=x.inte();
rep(i,k,min(n,k*2))x[i]+=(*this)[i];
rep(i,0,k)x[i]=0;
NTT(x,0);
rep(i,0,k*2)x[i]*=y[i];
NTT(x,1);
b.insert(b.end(),x.begin()+k,x.end());
} b.resize(n); return b;
}
Poly pow(ll t){
if(t==0){
Poly res(this->size()); res[0]=1;
return res;
}
int n=this->size(),k=0; while(k<n and (*this)[k]==0)k++;
Poly res(n); if(__int128_t(t)*k>=n)return res;
n-=t*k; Poly g(n); T c=(*this)[k],ic=c.inv();
rep(i,0,n)g[i]=(*this)[i+k]*ic;
g=g.log(); for(auto& x:g)x*=t; g=g.exp();
c=c.pow(t); rep(i,0,n)res[i+t*k]=g[i]*c; return res;
}
void NTT(vector<T>& a,bool inv)const;
};
/**
* @brief Formal Power Series (NTT-friendly mod)
*/
#line 7 "sol.cpp"
using Fp=fp<998244353>;
NTT<Fp,3> ntt;
template<>void Poly<Fp>::NTT(vector<Fp>& v,bool inv)const{return ntt.ntt(v,inv);}
#line 2 "library/FPS/samplepointshift.hpp"
template<typename T>Poly<T> SamplePointsShift(vector<T>& ys,T c,int m=-1){
ll n=ys.size()-1,C=c.v%T::get_mod();
if(m==-1)m=n+1;
factorial<T> fact(ys.size());
if(C<=n){
Poly<T> res;
rep(i,C,n+1)res.push_back(ys[i]);
if(int(res.size())>=m){
res.resize(m);
return res;
}
auto add=SamplePointsShift<T>(ys,n+1,m-res.size());
for(int i=0;int(res.size())<m;i++){
res.push_back(add[i]);
}
return res;
}
if(C+m>T::get_mod()){
auto res=SamplePointsShift<T>(ys,c,T::get_mod()-c.v);
auto add=SamplePointsShift<T>(ys,0,m-res.size());
rep(i,0,add.size())res.push_back(add[i]);
return res;
}
Poly<T> A(n+1),B(m+n);
rep(i,0,n+1){
A[i]=ys[i]*fact.fact(i,1)*fact.fact(n-i,1);
if((n-i)&1)A[i]=-A[i];
}
rep(i,0,m+n)B[i]=Fp(1)/(c-n+i);
auto AB=A*B;
vector<Fp> res(m);
Fp base=1;
rep(x,0,n+1)base*=(c-x);
rep(i,0,m){
res[i]=AB[n+i]*base;
base*=(c+i+1);
base*=B[i];
}
return res;
}
/**
* @brief Shift of Sampling Points of Polynomial
*/
#line 2 "library/Math/matrix.hpp"
template<class T>struct Matrix{
int h,w; vector<vector<T>> val; T det;
Matrix(){}
Matrix(int n):h(n),w(n),val(vector<vector<T>>(n,vector<T>(n))){}
Matrix(int n,int m):h(n),w(m),val(vector<vector<T>>(n,vector<T>(m))){}
vector<T>& operator[](const int i){return val[i];}
Matrix& operator+=(const Matrix& m){
assert(h==m.h and w==m.w);
rep(i,0,h)rep(j,0,w)val[i][j]+=m.val[i][j];
return *this;
}
Matrix& operator-=(const Matrix& m){
assert(h==m.h and w==m.w);
rep(i,0,h)rep(j,0,w)val[i][j]-=m.val[i][j];
return *this;
}
Matrix& operator*=(const Matrix& m){
assert(w==m.h);
Matrix<T> res(h,m.w);
rep(i,0,h)rep(j,0,m.w)rep(k,0,w)res.val[i][j]+=val[i][k]*m.val[k][j];
*this=res; return *this;
}
Matrix operator+(const Matrix& m)const{return Matrix(*this)+=m;}
Matrix operator-(const Matrix& m)const{return Matrix(*this)-=m;}
Matrix operator*(const Matrix& m)const{return Matrix(*this)*=m;}
Matrix pow(ll k){
Matrix<T> res(h,h),c=*this; rep(i,0,h)res.val[i][i]=1;
while(k){if(k&1)res*=c; c*=c; k>>=1;} return res;
}
vector<int> gauss(int c=-1){
if(val.empty())return {};
if(c==-1)c=w;
int cur=0; vector<int> res; det=1;
rep(i,0,c){
if(cur==h)break;
rep(j,cur,h)if(val[j][i]!=0){
swap(val[cur],val[j]);
if(cur!=j)det*=-1;
break;
}
det*=val[cur][i];
if(val[cur][i]==0)continue;
rep(j,0,h)if(j!=cur){
T z=val[j][i]/val[cur][i];
rep(k,i,w)val[j][k]-=val[cur][k]*z;
}
res.push_back(i);
cur++;
}
return res;
}
Matrix inv(){
assert(h==w);
Matrix base(h,h*2),res(h,h);
rep(i,0,h)rep(j,0,h)base[i][j]=val[i][j];
rep(i,0,h)base[i][h+i]=1;
base.gauss(h);
rep(i,0,h)rep(j,0,h)res[i][j]=base[i][h+j]/base[i][i];
return res;
}
bool operator==(const Matrix& m){
assert(h==m.h and w==m.w);
rep(i,0,h)rep(j,0,w)if(val[i][j]!=m.val[i][j])return false;
return true;
}
bool operator!=(const Matrix& m){
assert(h==m.h and w==m.w);
rep(i,0,h)rep(j,0,w)if(val[i][j]==m.val[i][j])return false;
return true;
}
friend istream& operator>>(istream& is,Matrix& m){
rep(i,0,m.h)rep(j,0,m.w)is>>m[i][j];
return is;
}
friend ostream& operator<<(ostream& os,Matrix& m){
rep(i,0,m.h){
rep(j,0,m.w)os<<m[i][j]<<(j==m.w-1 and i!=m.h-1?'\n':' ');
}
return os;
}
};
/**
* @brief Matrix
*/
#line 3 "library/Math/linearequation.hpp"
template<typename T>pair<vector<T>,Matrix<T>> LinearEquation(Matrix<T> a,vector<T> b){
int h=a.h,w=a.w;
rep(i,0,h)a[i].push_back(b[i]);
a.w++;
vector<int> idx=a.gauss(w);
rep(i,idx.size(),h)if(a[i][w]!=0)return {{},{}};
vector<T> res(w);
rep(i,0,idx.size())res[idx[i]]=a[i][w]/a[i][idx[i]];
Matrix<T> d(w,h+w);
rep(i,0,h)rep(j,0,w)d[j][i]=a[i][j];
rep(i,0,w)d[i][h+i]=1;
int r=d.gauss(h).size();
Matrix<T> basis(w-r,w);
rep(i,r,w)basis[i-r]={d[i].begin()+h,d[i].end()};
return {res,basis};
}
/**
* @brief Linear Equation
*/
#line 5 "library/FPS/p-recursive.hpp"
template<typename T>Matrix<T> PrefixProdOfPolyMatrix(Matrix<Poly<T>>& m,ll K){
using Mat=Matrix<T>;
int n=m.val.size();
int deg=1;
rep(i,0,n)rep(j,0,n)chmax(deg,(int)m[i][j].size()-1);
ll SQ=1;
while(SQ*SQ*deg<K)SQ<<=1;
T iSQ=T(SQ).inv();
vector<Mat> G(deg+1);
rep(k,0,deg+1){
G[k]=Mat(n,n);
rep(i,0,n)rep(j,0,n)G[k][i][j]=m[i][j].eval(SQ*k);
}
auto process=[&](vector<Mat>& base,T x)->vector<Mat>{
int D=base.size();
vector ret(D,Mat(n,n));
rep(i,0,n)rep(j,0,n){
vector<T> val(D);
rep(k,0,D)val[k]=base[k][i][j];
auto add=SamplePointsShift<T>(val,x);
rep(k,0,D)ret[k][i][j]=add[k];
}
return ret;
};
for(ll w=1;w<SQ;w<<=1){
auto G1=process(G,iSQ*w);
auto G2=process(G,w*deg+1);
auto G3=process(G,iSQ*w+w*deg+1);
rep(i,0,w*deg+1)G1[i]*=G[i],G3[i]*=G2[i];
G1.insert(G1.end(),ALL(G3));
G1.pop_back();
swap(G,G1);
}
Mat ret(n,n);
rep(i,0,n)ret[i][i]=1;
ll k=0;
while(k*SQ+SQ<=K)ret=G[k++]*ret;
k*=SQ;
while(k<K){
Mat mul(n,n);
rep(i,0,n)rep(j,0,n)mul[i][j]=m[i][j].eval(k);
ret=mul*ret;
k++;
}
return ret;
}
// a_{n+i}*f_n(i)+...+a_i*f_0(i)=0
// {f_r}:dec order!!!
template<typename T>vector<Poly<T>> FindPRecursive(vector<T>& a,int d){
int n=a.size();
int k=(n+2)/(d+2)-1;
if(k<=0)return {};
int m=(d+1)*(k+1);
Matrix<T> mat(m-1,m);
rep(i,0,m-1)rep(j,0,k+1){
T base=1;
rep(deg,0,d+1){
mat[i][(d+1)*j+deg]=a[i+j]*base;
base*=(i+j);
}
}
auto basis=LinearEquation(mat,vector<T>(m-1)).second;
if(basis.val.empty())return {};
auto c=basis[0];
vector<Poly<T>> ret;
for(int i=0;i*(d+1)<(int)c.size();i++){
Poly<T> add,base({T(i),T(1)});
for(int j=d;j>=0;j--){
add*=base;
if(c[i*(d+1)+j]!=0)add+=c[i*(d+1)+j];
}
ret.push_back(add);
}
while(ret.back().empty())ret.pop_back();
reverse(ALL(ret));
return ret;
}
template<typename T>T KthtermOfPRecursive(vector<T>& a,vector<Poly<T>>& fs,ll k){
int n=fs.size()-1;
assert(int(a.size())>=n);
if(k<int(a.size()))return a[k];
Matrix<Poly<T>> m(n),den(1);
Matrix<T> base(n);
rep(i,0,n)m[0][i]=-fs[i+1];
rep(i,1,n)m[i][i-1]=fs[0];
den[0][0]=fs[0];
rep(i,0,n)base[i][0]=a[n-1-i];
T ret=(PrefixProdOfPolyMatrix(m,k-n+1)*base)[0][0];
ret/=PrefixProdOfPolyMatrix(den,k-n+1)[0][0];
return ret;
}
template<typename T>T KthtermEsper(vector<T>& a,ll k){
if(k<(int)a.size())return a[k];
int n=a.size()-1;
vector<Fp> b=a;
b.pop_back();
for(int d=0;;d++){
if((n+2)/(d+2)<=1)break;
auto fs=FindPRecursive(b,d);
if(KthtermOfPRecursive(b,fs,n)==a.back()){
return KthtermOfPRecursive(a,fs,k);
}
}
cerr<<"esper Failed"<<'\n';
assert(0);
}
/**
* @brief P-recursive
*/
#line 2 "library/FPS/multieval.hpp"
template<typename T>struct MultiEval{
int m,n; vector<Poly<T>> t;
MultiEval(vector<T>& v){
m=v.size(),n=1; while(n<m)n<<=1;
t.resize(n<<1);
rep(i,0,n){
T w=(i<m?v[i]:0);
t[n+i]=Poly<T>({-w,T(1)});
}
for(int i=n-1;i;i--)t[i]=t[i*2]*t[i*2+1];
}
vector<T> run(const vector<T>& f){
if(f.empty())return vector<T>(m);
vector<Poly<T>> c(n*2);
auto v=t[1].rev();
v.resize(f.size());
v=v.inv().rev()*Poly<T>(f);
v.erase(v.begin(),v.begin()+f.size()-1);
v.resize(n); reverse(ALL(v)); c[1]=v;
rep(i,1,n){
int d=c[i].size();
rep(k,0,2){
auto add=t[i*2+(k^1)];
add.resize(d/2+1);
add=add.rev();
add*=c[i];
add.resize(d);
c[i*2+k]=vector<T>(add.begin()+d/2,add.end());
}
}
vector<T> res(m); rep(i,0,m)res[i]=c[n+i][0];
return res;
}
vector<T> build(vector<T>& ys){
auto w=t[1].rev();
w.resize(m+1);
auto vs=run(w.rev().diff());
rep(i,0,m)ys[i]/=vs[i];
vector<Poly<T>> c(n*2);
rep(i,0,n){
if(i<m)c[n+i]=Poly<T>({ys[i]});
else c[n+i]=Poly<T>({T()});
}
for(int i=n-1;i;i--)c[i]=c[i*2]*t[i*2+1]+c[i*2+1]*t[i*2];
c[1]=vector<T>(c[1].begin()+(n-m),c[1].end());
c[1].resize(m);
return c[1];
}
};
/**
* @brief Multipoint Evaluation
*/
#line 13 "sol.cpp"
FastIO io;
void solve1(int t){
vector<ll> n(t),k(t);
rep(i,0,t)io.read(n[i],k[i]);
int m=1<<17;
vector<Poly<Fp>> subprod(m*2,Poly<Fp>({Fp(1)}));
using P=pair<ll,ll>;
vector que(m,vector<P>());
rep(i,0,t){
que[k[i]].push_back({n[i],i});
}
rep(k,0,m)if(que[k].size()){
deque<Poly<Fp>> deq;
for(auto& [N,_]:que[k])deq.push_back(Poly<Fp>({Fp(-N),Fp(1)}));
while(deq.size()>1){
auto A=deq.front();
deq.pop_front();
auto B=deq.front();
deq.pop_front();
deq.push_back(A*B);
}
subprod[m+k]=deq.front();
}
for(int i=m-1;i;i--)subprod[i]=subprod[i*2]*subprod[i*2+1];
vector<Fp> ret(t);
vector mat(m*2,Matrix<Poly<Fp>>(2)),rui(m*2,Matrix<Poly<Fp>>(2));
auto dfs=[&](auto& dfs,int L,int R,int id)->void{
if(R-L==1){
if(que[L].size()){
vector<Fp> xs;
for(auto& [x,_]:que[L])xs.push_back(x);
MultiEval<Fp> buf(xs);
auto ys=buf.run(mat[id][0][0]%subprod[id]);
rep(i,0,que[L].size())ret[que[L][i].second]=ys[i];
}
rui[id][0][0]=Poly<Fp>({Fp(-2*L),Fp(2)});
rui[id][0][1]=Poly<Fp>({Fp(-L)*(L-1)/2,Fp(L)});
rui[id][1][0]=Poly<Fp>({Fp(1)});
return;
}
int mid=(L+R)>>1;
rep(i,0,2)rep(j,0,2)mat[id*2][i][j]=mat[id][i][j]%subprod[id];
dfs(dfs,L,mid,id*2);
mat[id*2+1]=rui[id*2]*mat[id*2];
dfs(dfs,mid,R,id*2+1);
rui[id]=rui[id*2+1]*rui[id*2];
return;
};
mat[1][0][0]=mat[1][1][1]=Poly<Fp>({Fp(1)});
dfs(dfs,0,m,1);
rep(i,0,t)io.write(ret[i].v);
}
void solve2(int t){
while(t--){
ll n,k;
io.read(n,k);
if(k>=Fp::get_mod())io.write(0);
else{
vector<Fp> a(2);
a[0]=1,a[1]=n*2;
vector<Poly<Fp>> fs(3);
fs[0]=Poly<Fp>({Fp(1)});
fs[1]=Poly<Fp>({-n*2+2,2});
fs[2]=Poly<Fp>({-n,Fp(1-n*2)/2,Fp(1)/2});
Fp ret=KthtermOfPRecursive(a,fs,k);
io.write(ret.v);
}
}
}
int main(){
int t;
io.read(t);
if(t>5)solve1(t);
else solve2(t);
return 0;
}