#ifndef LOCAL
#pragma GCC optimize ("Ofast")
#pragma GCC optimize ("unroll-loops")
#endif

#include <bits/stdc++.h>
using namespace std;

using ll=long long;
#define int ll

#define rng(i,a,b) for(int i=int(a);i<int(b);i++)
#define rep(i,b) rng(i,0,b)
#define gnr(i,a,b) for(int i=int(b)-1;i>=int(a);i--)
#define per(i,b) gnr(i,0,b)
#define pb push_back
#define eb emplace_back
#define a first
#define b second
#define bg begin()
#define ed end()
#define all(x) x.bg,x.ed
#define si(x) int(x.size())
#ifdef LOCAL
#define dmp(x) cerr<<__LINE__<<" "<<#x<<" "<<x<<endl
#else
#define dmp(x) void(0)
#endif

template<class t,class u> bool chmax(t&a,u b){if(a<b){a=b;return true;}else return false;}
template<class t,class u> bool chmin(t&a,u b){if(b<a){a=b;return true;}else return false;}

template<class t> using vc=vector<t>;
template<class t> using vvc=vc<vc<t>>;

using pi=pair<int,int>;
using vi=vc<int>;

template<class t,class u>
ostream& operator<<(ostream& os,const pair<t,u>& p){
	return os<<"{"<<p.a<<","<<p.b<<"}";
}

template<class t> ostream& operator<<(ostream& os,const vc<t>& v){
	os<<"{";
	for(auto e:v)os<<e<<",";
	return os<<"}";
}

#define mp make_pair
#define mt make_tuple
#define one(x) memset(x,-1,sizeof(x))
#define zero(x) memset(x,0,sizeof(x))
#ifdef LOCAL
void dmpr(ostream&os){os<<endl;}
template<class T,class... Args>
void dmpr(ostream&os,const T&t,const Args&... args){
	os<<t<<" ";
	dmpr(os,args...);
}
#define dmp2(...) dmpr(cerr,__LINE__,##__VA_ARGS__)
#else
#define dmp2(...) void(0)
#endif

using uint=unsigned;
using ull=unsigned long long;

template<class t,size_t n>
ostream& operator<<(ostream&os,const array<t,n>&a){
	return os<<vc<t>(all(a));
}

template<int i,class T>
void print_tuple(ostream&,const T&){
}

template<int i,class T,class H,class ...Args>
void print_tuple(ostream&os,const T&t){
	if(i)os<<",";
	os<<get<i>(t);
	print_tuple<i+1,T,Args...>(os,t);
}

template<class ...Args>
ostream& operator<<(ostream&os,const tuple<Args...>&t){
	os<<"{";
	print_tuple<0,tuple<Args...>,Args...>(os,t);
	return os<<"}";
}

template<class t>
void print(t x,int suc=1){
	cout<<x;
	if(suc==1)
		cout<<"\n";
	if(suc==2)
		cout<<" ";
}

ll read(){
	ll i;
	cin>>i;
	return i;
}

vi readvi(int n,int off=0){
	vi v(n);
	rep(i,n)v[i]=read()+off;
	return v;
}

pi readpi(int off=0){
	int a,b;cin>>a>>b;
	return pi(a+off,b+off);
}

template<class t,class u>
void print(const pair<t,u>&p,int suc=1){
	print(p.a,2);
	print(p.b,suc);
}

template<class t,class u>
void print_offset(const pair<t,u>&p,ll off,int suc=1){
	print(p.a+off,2);
	print(p.b+off,suc);
}

template<class T>
void print(const vector<T>&v,int suc=1){
	rep(i,v.size())
		print(v[i],i==int(v.size())-1?suc:2);
}

template<class T>
void print_offset(const vector<T>&v,ll off,int suc=1){
	rep(i,v.size())
		print(v[i]+off,i==int(v.size())-1?suc:2);
}

template<class T,size_t N>
void print(const array<T,N>&v,int suc=1){
	rep(i,N)
		print(v[i],i==int(N)-1?suc:2);
}

string readString(){
	string s;
	cin>>s;
	return s;
}

template<class T>
T sq(const T& t){
	return t*t;
}

void YES(bool ex=true){
	cout<<"YES\n";
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}
void NO(bool ex=true){
	cout<<"NO\n";
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}
void Yes(bool ex=true){
	cout<<"Yes\n";
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}
void No(bool ex=true){
	cout<<"No\n";
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}
//#define CAPITAL
/*
void yes(bool ex=true){
	#ifdef CAPITAL
	cout<<"YES"<<"\n";
	#else
	cout<<"Yes"<<"\n";
	#endif
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}
void no(bool ex=true){
	#ifdef CAPITAL
	cout<<"NO"<<"\n";
	#else
	cout<<"No"<<"\n";
	#endif
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}*/
void possible(bool ex=true){
	#ifdef CAPITAL
	cout<<"POSSIBLE"<<"\n";
	#else
	cout<<"Possible"<<"\n";
	#endif
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}
void impossible(bool ex=true){
	#ifdef CAPITAL
	cout<<"IMPOSSIBLE"<<"\n";
	#else
	cout<<"Impossible"<<"\n";
	#endif
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}

constexpr ll ten(int n){
	return n==0?1:ten(n-1)*10;
}

const ll infLL=LLONG_MAX/3;

#ifdef int
const int inf=infLL;
#else
const int inf=INT_MAX/2-100;
#endif

int topbit(signed t){
	return t==0?-1:31-__builtin_clz(t);
}
int topbit(ll t){
	return t==0?-1:63-__builtin_clzll(t);
}
int botbit(signed a){
	return a==0?32:__builtin_ctz(a);
}
int botbit(ll a){
	return a==0?64:__builtin_ctzll(a);
}
int botbit(ull a){
	return a==0?64:__builtin_ctzll(a);
}
int popcount(signed t){
	return __builtin_popcount(t);
}
int popcount(ll t){
	return __builtin_popcountll(t);
}
int popcount(ull t){
	return __builtin_popcountll(t);
}
bool ispow2(int i){
	return i&&(i&-i)==i;
}
ll mask(int i){
	return (ll(1)<<i)-1;
}

bool inc(int a,int b,int c){
	return a<=b&&b<=c;
}

template<class t> void mkuni(vc<t>&v){
	sort(all(v));
	v.erase(unique(all(v)),v.ed);
}

ll rand_int(ll l, ll r) { //[l, r]
	#ifdef LOCAL
	static mt19937_64 gen;
	#else
	static mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());
	#endif
	return uniform_int_distribution<ll>(l, r)(gen);
}

template<class t>
void myshuffle(vc<t>&a){
	rep(i,si(a))swap(a[i],a[rand_int(0,i)]);
}

template<class t>
int lwb(const vc<t>&v,const t&a){
	return lower_bound(all(v),a)-v.bg;
}

vvc<int> readGraph(int n,int m){
	vvc<int> g(n);
	rep(i,m){
		int a,b;
		cin>>a>>b;
		//sc.read(a,b);
		a--;b--;
		g[a].pb(b);
		g[b].pb(a);
	}
	return g;
}

vvc<int> readTree(int n){
	return readGraph(n,n-1);
}

vc<ll> presum(const vi&a){
	vc<ll> s(si(a)+1);
	rep(i,si(a))s[i+1]=s[i]+a[i];
	return s;
}

//mint107 は verify してねえ
//#define DYNAMIC_MOD

struct modinfo{uint mod,root;
#ifdef DYNAMIC_MOD
constexpr modinfo(uint m,uint r):mod(m),root(r),im(0){set_mod(m);}
ull im;
constexpr void set_mod(uint m){
	mod=m;
	im=ull(-1)/m+1;
}
uint product(uint a,uint b)const{
	ull z=ull(a)*b;
	uint x=((unsigned __int128)z*im)>>64;
	uint v=uint(z)-x*mod;
	return v<mod?v:v+mod;
}
#endif
};
template<modinfo const&ref>
struct modular{
	static constexpr uint const &mod=ref.mod;
	static modular root(){return modular(ref.root);}
	uint v;
	//modular(initializer_list<uint>ls):v(*ls.bg){}
	modular(ll vv=0){s(vv%mod+mod);}
	modular& s(uint vv){
		v=vv<mod?vv:vv-mod;
		return *this;
	}
	modular operator-()const{return modular()-*this;}
	modular& operator+=(const modular&rhs){return s(v+rhs.v);}
	modular&operator-=(const modular&rhs){return s(v+mod-rhs.v);}
	modular&operator*=(const modular&rhs){
		#ifndef DYNAMIC_MOD
		v=ull(v)*rhs.v%mod;
		#else
		v=ref.product(v,rhs.v);
		#endif
		return *this;
	}
	modular&operator/=(const modular&rhs){return *this*=rhs.inv();}
	modular operator+(const modular&rhs)const{return modular(*this)+=rhs;}
	modular operator-(const modular&rhs)const{return modular(*this)-=rhs;}
	modular operator*(const modular&rhs)const{return modular(*this)*=rhs;}
	modular operator/(const modular&rhs)const{return modular(*this)/=rhs;}
	modular pow(ll n)const{
		if(n<0)return inv().pow(-n);
		modular res(1),x(*this);
		while(n){
			if(n&1)res*=x;
			x*=x;
			n>>=1;
		}
		return res;
	}
	modular inv()const{return pow(mod-2);}
	/*modular inv()const{
		int x,y;
		int g=extgcd<ll>(v,mod,x,y);
		assert(g==1);
		if(x<0)x+=mod;
		return modular(x);
	}*/
	friend modular operator+(ll x,const modular&y){
		return modular(x)+y;
	}
	friend modular operator-(ll x,const modular&y){
		return modular(x)-y;
	}
	friend modular operator*(ll x,const modular&y){
		return modular(x)*y;
	}
	friend modular operator/(ll x,const modular&y){
		return modular(x)/y;
	}
	friend ostream& operator<<(ostream&os,const modular&m){
		return os<<m.v;
	}
	friend istream& operator>>(istream&is,modular&m){
		ll x;is>>x;
		m=modular(x);
		return is;
	}
	bool operator<(const modular&r)const{return v<r.v;}
	bool operator==(const modular&r)const{return v==r.v;}
	bool operator!=(const modular&r)const{return v!=r.v;}
	explicit operator bool()const{
		return v;
	}
};

#define USE_GOOD_MOD

//size of input must be a power of 2
//output of forward fmt is bit-reversed
//output elements are in the range [0,mod*4)
//input of inverse fmt should be bit-reversed
template<class mint>
void inplace_fmt(const int n,mint*const f,bool inv){
	static constexpr uint mod=mint::mod;
	static constexpr uint mod2=mod*2;
	static constexpr int L=30;
	static mint g[L],ig[L],p2[L];
	if(g[0].v==0){
		rep(i,L){
			mint w=-mint::root().pow(((mod-1)>>(i+2))*3);
			g[i]=w;
			ig[i]=w.inv();
			p2[i]=mint(1<<i).inv();
		}
	}
	if(!inv){
		int b=n;
		if(b>>=1){//input:[0,mod)
			rep(i,b){
				uint x=f[i+b].v;
				f[i+b].v=f[i].v+mod-x;
				f[i].v+=x;
			}
		}
		if(b>>=1){//input:[0,mod*2)
			mint p=1;
			for(int i=0,k=0;i<n;i+=b*2){
				rng(j,i,i+b){
					uint x=(f[j+b]*p).v;
					f[j+b].v=f[j].v+mod-x;
					f[j].v+=x;
				}
				p*=g[__builtin_ctz(++k)];
			}
		}
		while(b){
			if(b>>=1){//input:[0,mod*3)
				mint p=1;
				for(int i=0,k=0;i<n;i+=b*2){
					rng(j,i,i+b){
						uint x=(f[j+b]*p).v;
						f[j+b].v=f[j].v+mod-x;
						f[j].v+=x;
					}
					p*=g[__builtin_ctz(++k)];
				}
			}
			if(b>>=1){//input:[0,mod*4)
				mint p=1;
				for(int i=0,k=0;i<n;i+=b*2){
					rng(j,i,i+b){
						uint x=(f[j+b]*p).v;
						f[j].v=(f[j].v<mod2?f[j].v:f[j].v-mod2);
						f[j+b].v=f[j].v+mod-x;
						f[j].v+=x;
					}
					p*=g[__builtin_ctz(++k)];
				}
			}
		}
	}else{
		int b=1;
		if(b<n/2){//input:[0,mod)
			mint p=1;
			for(int i=0,k=0;i<n;i+=b*2){
				rng(j,i,i+b){
					ull x=f[j].v+mod-f[j+b].v;
					f[j].v+=f[j+b].v;
					f[j+b].v=x*p.v%mod;
				}
				p*=ig[__builtin_ctz(++k)];
			}
			b<<=1;
		}
		for(;b<n/2;b<<=1){
			mint p=1;
			for(int i=0,k=0;i<n;i+=b*2){
				rng(j,i,i+b/2){//input:[0,mod*2)
					ull x=f[j].v+mod2-f[j+b].v;
					f[j].v+=f[j+b].v;
					f[j].v=(f[j].v)<mod2?f[j].v:f[j].v-mod2;
					f[j+b].v=x*p.v%mod;
				}
				rng(j,i+b/2,i+b){//input:[0,mod)
					ull x=f[j].v+mod-f[j+b].v;
					f[j].v+=f[j+b].v;
					f[j+b].v=x*p.v%mod;
				}
				p*=ig[__builtin_ctz(++k)];
			}
		}
		if(b<n){//input:[0,mod*2)
			rep(i,b){
				uint x=f[i+b].v;
				f[i+b].v=f[i].v+mod2-x;
				f[i].v+=x;
			}
		}
		mint z=p2[__lg(n)];
		rep(i,n)f[i]*=z;
	}
}

template<class mint>
void inplace_fmt(vector<mint>&f,bool inv){
	inplace_fmt(si(f),f.data(),inv);
}

//size of input must be a power of 2
//output elements are in the range [0,mod*4)
template<class mint>
void half_fmt(const int n,mint*const f){
	static constexpr uint mod=mint::mod;
	static constexpr uint mod2=mod*2;
	static const int L=30;
	static mint g[L],h[L];
	if(g[0].v==0){
		rep(i,L){
			g[i]=-mint::root().pow(((mod-1)>>(i+2))*3);
			h[i]=mint::root().pow((mod-1)>>(i+2));
		}
	}
	int b=n;
	int lv=0;
	if(b>>=1){//input:[0,mod)
		mint p=h[lv++];
		for(int i=0,k=0;i<n;i+=b*2){
			rng(j,i,i+b){
				uint x=(f[j+b]*p).v;
				f[j+b].v=f[j].v+mod-x;
				f[j].v+=x;
			}
			p*=g[__builtin_ctz(++k)];
		}
	}
	if(b>>=1){//input:[0,mod*2)
		mint p=h[lv++];
		for(int i=0,k=0;i<n;i+=b*2){
			rng(j,i,i+b){
				uint x=(f[j+b]*p).v;
				f[j+b].v=f[j].v+mod-x;
				f[j].v+=x;
			}
			p*=g[__builtin_ctz(++k)];
		}
	}
	while(b){
		if(b>>=1){//input:[0,mod*3)
			mint p=h[lv++];
			for(int i=0,k=0;i<n;i+=b*2){
				rng(j,i,i+b){
					uint x=(f[j+b]*p).v;
					f[j+b].v=f[j].v+mod-x;
					f[j].v+=x;
				}
				p*=g[__builtin_ctz(++k)];
			}
		}
		if(b>>=1){//input:[0,mod*4)
			mint p=h[lv++];
			for(int i=0,k=0;i<n;i+=b*2){
				rng(j,i,i+b){
					uint x=(f[j+b]*p).v;
					f[j].v=(f[j].v<mod2?f[j].v:f[j].v-mod2);
					f[j+b].v=f[j].v+mod-x;
					f[j].v+=x;
				}
				p*=g[__builtin_ctz(++k)];
			}
		}
	}
}

template<class mint>
void half_fmt(vector<mint>&f){
	half_fmt(si(f),f.data());
}

#ifdef USE_GOOD_MOD

template<class mint>
vc<mint> multiply(vc<mint> x,const vc<mint>&y,bool same=false){
	int n=si(x)+si(y)-1;
	int s=1;
	while(s<n)s*=2;
	x.resize(s);inplace_fmt(x,false);
	if(!same){
		static vc<mint> z;
		z.clear();z.resize(s);
		rep(i,si(y))z[i]=y[i];
		inplace_fmt(z,false);
		rep(i,s)x[i]*=z[i];
	}else{
		rep(i,s)x[i]*=x[i];
	}
	inplace_fmt(x,true);x.resize(n);
	return x;
}
template<class mint>
vc<mint> multiply_givenlength(vc<mint> x,const vc<mint>&y,bool same=false){
	int s=si(x);
	assert(ispow2(s));
	assert(si(y));
	x.resize(s);inplace_fmt(x,false);
	if(!same){
		vc<mint> z(s);
		rep(i,si(y))z[i]=y[i];
		inplace_fmt(z,false);
		rep(i,s)x[i]*=z[i];
	}else{
		rep(i,s)x[i]*=x[i];
	}
	inplace_fmt(x,true);
	return x;
}

#else

//59501818244292734739283969-1=5.95*10^25 までの値を正しく計算
//最終的な列の大きさが 2^24 までなら動く
//最終的な列の大きさが 2^20 以下のときは，下の 3 つの素数を使ったほうが速い（は？）
//VERIFY: yosupo
//Yukicoder No980 (same=true)
namespace arbitrary_convolution{
	constexpr modinfo base0{167772161,3};//2^25 * 5 + 1
	constexpr modinfo base1{469762049,3};//2^26 * 7 + 1
	constexpr modinfo base2{754974721,11};//2^24 * 45 + 1
	//extern constexpr modinfo base0{1045430273,3};//2^20 * 997 + 1
	//extern constexpr modinfo base1{1051721729,6};//2^20 * 1003 + 1
	//extern constexpr modinfo base2{1053818881,7};//2^20 * 1005 + 1
	using mint0=modular<base0>;
	using mint1=modular<base1>;
	using mint2=modular<base2>;
	template<class t,class mint>
	vc<t> sub(const vc<mint>&x,const vc<mint>&y,bool same=false){
		int n=si(x)+si(y)-1;
		int s=1;
		while(s<n)s*=2;
		vc<t> z(s);rep(i,si(x))z[i]=x[i].v;
		inplace_fmt(z,false);
		if(!same){
			vc<t> w(s);rep(i,si(y))w[i]=y[i].v;
			inplace_fmt(w,false);
			rep(i,s)z[i]*=w[i];
		}else{
			rep(i,s)z[i]*=z[i];
		}
		inplace_fmt(z,true);z.resize(n);
		return z;
	}
	template<class mint>
	vc<mint> multiply(const vc<mint>&x,const vc<mint>&y,bool same=false){
		auto d0=sub<mint0>(x,y,same);
		auto d1=sub<mint1>(x,y,same);
		auto d2=sub<mint2>(x,y,same);
		int n=si(d0);
		vc<mint> res(n);
		static const mint1 r01=mint1(mint0::mod).inv();
		static const mint2 r02=mint2(mint0::mod).inv();
		static const mint2 r12=mint2(mint1::mod).inv();
		static const mint2 r02r12=r02*r12;
		static const mint w1=mint(mint0::mod);
		static const mint w2=w1*mint(mint1::mod);
		rep(i,n){
			ull a=d0[i].v;
			ull b=(d1[i].v+mint1::mod-a)*r01.v%mint1::mod;
			ull c=((d2[i].v+mint2::mod-a)*r02r12.v+(mint2::mod-b)*r12.v)%mint2::mod;
			res[i].v=(a+b*w1.v+c*w2.v)%mint::mod;
		}
		return res;
	}
	template<class t,class mint>
	vc<t> sub_givenlength(const vc<mint>&x,const vc<mint>&y,bool same=false){
		int s=si(x);
		assert(ispow2(s));
		assert(si(y)==s);
		vc<t> z(s);rep(i,si(x))z[i]=x[i].v;
		inplace_fmt(z,false);
		if(!same){
			vc<t> w(s);rep(i,si(y))w[i]=y[i].v;
			inplace_fmt(w,false);
			rep(i,s)z[i]*=w[i];
		}else{
			rep(i,s)z[i]*=z[i];
		}
		inplace_fmt(z,true);
		return z;
	}
	template<class mint>
	vc<mint> multiply_givenlength(const vc<mint>&x,const vc<mint>&y,bool same=false){
		auto d0=sub_givenlength<mint0>(x,y,same);
		auto d1=sub_givenlength<mint1>(x,y,same);
		auto d2=sub_givenlength<mint2>(x,y,same);
		int n=si(d0);
		vc<mint> res(n);
		static const mint1 r01=mint1(mint0::mod).inv();
		static const mint2 r02=mint2(mint0::mod).inv();
		static const mint2 r12=mint2(mint1::mod).inv();
		static const mint2 r02r12=r02*r12;
		static const mint w1=mint(mint0::mod);
		static const mint w2=w1*mint(mint1::mod);
		rep(i,n){
			ull a=d0[i].v;
			ull b=(d1[i].v+mint1::mod-a)*r01.v%mint1::mod;
			ull c=((d2[i].v+mint2::mod-a)*r02r12.v+(mint2::mod-b)*r12.v)%mint2::mod;
			res[i].v=(a+b*w1.v+c*w2.v)%mint::mod;
		}
		return res;
	}
}
using arbitrary_convolution::multiply;
using arbitrary_convolution::multiply_givenlength;

#endif

//UTPC2021 C
namespace integer_convolution{
	extern constexpr modinfo base0{1045430273,3};//2^20 * 997 + 1
	extern constexpr modinfo base1{1051721729,6};//2^20 * 1003 + 1
	//extern constexpr modinfo base0{469762049,3};//2^26 * 7 + 1
	//extern constexpr modinfo base1{754974721,11};//2^24 * 45 + 1
	using mint0=modular<base0>;
	using mint1=modular<base1>;
	template<class t>
	vc<t> sub(const vi&x,const vi&y,bool same=false){
		int n=si(x)+si(y)-1;
		int s=1;
		while(s<n)s*=2;
		vc<t> z(s);rep(i,si(x))z[i]=x[i];
		inplace_fmt(z,false);
		if(!same){
			vc<t> w(s);rep(i,si(y))w[i]=y[i];
			inplace_fmt(w,false);
			rep(i,s)z[i]*=w[i];
		}else{
			rep(i,s)z[i]*=z[i];
		}
		inplace_fmt(z,true);z.resize(n);
		return z;
	}
	vi multiply(const vi&x,const vi&y,bool same=false){
		auto d0=sub<mint0>(x,y,same);
		auto d1=sub<mint1>(x,y,same);
		const mint1 r=mint1(mint0::mod).inv();
		const ll v=ll(mint0::mod)*mint1::mod;
		int n=si(d0);
		vi res(n);
		rep(i,n){
			res[i]=d0[i].v+(r*(d1[i]-d0[i].v)).v*(ull)mint0::mod;
			if(res[i]>v/2)res[i]-=v;
		}
		return res;
	}
}

//最大で 1<<mx のサイズの fft が登場！
template<class mint>
vc<mint> large_convolution(const vc<mint>&a,const vc<mint>&b,int mx){
	int n=si(a),m=si(b);
	vc<mint> c(n+m-1);
	int len=1<<(mx-1);
	for(int i=0;i<n;i+=len){
		for(int j=0;j<n;j+=len){
			int x=min(len,n-i),y=min(len,m-j);
			auto d=multiply(vc<mint>(a.bg+i,a.bg+i+x),vc<mint>(b.bg+j,b.bg+j+y));
			rep(k,si(d))
				c[i+j+k]+=d[k];
		}
	}
	return c;
}

//input A: N 次,B ?,M
//output D: M 次多項式
//C を M 次多項式として
//[x^N] A*B*C = [x^M] D*C
//となるような D を返す
//CF796F
template<class mint>
vc<mint> transpose_advance(const vc<mint>&a,const vc<mint>&b,int m){
	int n=si(a)-1;
	auto d=multiply(a,b);
	vc<mint> res(m+1);
	if(n>=m){
		rep(i,m+1)res[i]=d[i+n-m];
	}else{
		rng(i,m-n,m+1)res[i]=d[i+n-m];
	}
	return res;
}

template<class mint>
void chmult(vc<mint>&x,const vc<mint>&y,int s){
	x=multiply(move(x),y);
	x.resize(s);
}

//Poly というのは常にサイズ 1 以上であることにしよう
//low のあたりをかならずサイズ s のものを返すようにいじった
//その影響で何かが起きているかも知れないし，起きていないかも知れない
template<class mint>
struct Poly:public vc<mint>{
	template<class...Args>
	Poly(Args...args):vc<mint>(args...){}
	Poly(initializer_list<mint>init):vc<mint>(all(init)){}
	int size()const{
		return vc<mint>::size();
	}
	void ups(int s){
		if(size()<s)this->resize(s,0);
	}
	Poly low(int s)const{
		assert(s);
		Poly res(s);
		rep(i,min(s,size()))res[i]=(*this)[i];
		return res;
	}
	Poly rev()const{
		auto r=*this;
		reverse(all(r));
		return r;
	}
	Poly operator>>(int x)const{
		assert(x<size());
		Poly res(size()-x);
		rep(i,size()-x)res[i]=(*this)[i+x];
		return res;
	}
	Poly operator<<(int x)const{
		Poly res(size()+x);
		rep(i,size())res[i+x]=(*this)[i];
		return res;
	}
	mint freq(int i)const{
		return i<size()?(*this)[i]:0;
	}
	Poly operator-()const{
		Poly res=*this;
		for(auto&v:res)v=-v;
		return res;
	}
	Poly& operator+=(const Poly&r){
		ups(r.size());
		rep(i,r.size())
			(*this)[i]+=r[i];
		return *this;
	}
	template<class T>
	Poly& operator+=(T t){
		(*this)[0]+=t;
		return *this;
	}
	Poly& operator-=(const Poly&r){
		ups(r.size());
		rep(i,r.size())
			(*this)[i]-=r[i];
		return *this;
	}
	template<class T>
	Poly& operator-=(T t){
		(*this)[0]-=t;
		return *this;
	}
	template<class T>
	Poly& operator*=(T t){
		for(auto&v:*this)
			v*=t;
		return *this;
	}
	Poly& operator*=(const Poly&r){
		return *this=multiply(*this,r);
	}
	Poly square()const{
		return multiply(*this,*this,true);
	}
	#ifndef USE_GOOD_MOD
	Poly inv(int s)const{
		Poly r{mint(1)/(*this)[0]};
		for(int n=1;n<s;n*=2)
			r=r*2-(r.square()*low(2*n)).low(2*n);
		r.resize(s);
		return r;
	}
	#else
	//source: Section 4 of "Removing redundancy from high-precision Newton iteration"
	// 5/3
	Poly inv(int s)const{
		Poly r(s);
		r[0]=mint(1)/(*this)[0];
		for(int n=1;n<s;n*=2){
			vc<mint> f=low(2*n);
			f.resize(2*n);
			inplace_fmt(f,false);
			vc<mint> g=r.low(2*n);
			g.resize(2*n);
			inplace_fmt(g,false);
			rep(i,2*n)f[i]*=g[i];
			inplace_fmt(f,true);
			rep(i,n)f[i]=0;
			inplace_fmt(f,false);
			rep(i,2*n)f[i]*=g[i];
			inplace_fmt(f,true);
			rng(i,n,min(2*n,s))r[i]=-f[i];
		}
		return r;
	}
	#endif
	template<class T>
	Poly& operator/=(T t){
		return *this*=mint(1)/mint(t);
	}
	Poly quotient(const Poly&r,const Poly&rri)const{
		int m=r.size();
		assert(r[m-1].v);
		int n=size();
		int s=n-m+1;
		if(s<=0) return {0};
		return (rev().low(s)*rri.low(s)).low(s).rev();
	}
	Poly& operator/=(const Poly&r){
		return *this=quotient(r,r.rev().inv(max(size()-r.size(),int(0))+1));
	}
	Poly& operator%=(const Poly&r){
		*this-=*this/r*r;
		return *this=low(r.size()-1);
	}
	Poly operator+(const Poly&r)const{return Poly(*this)+=r;}
	template<class T>
	Poly operator+(T t)const{return Poly(*this)+=t;}
	Poly operator-(const Poly&r)const{return Poly(*this)-=r;}
	template<class T>
	Poly operator-(T t)const{return Poly(*this)-=t;}
	template<class T>
	Poly operator*(T t)const{return Poly(*this)*=t;}
	Poly operator*(const Poly&r)const{return Poly(*this)*=r;}
	template<class T>
	Poly operator/(T t)const{return Poly(*this)/=t;}
	Poly operator/(const Poly&r)const{return Poly(*this)/=r;}
	Poly operator%(const Poly&r)const{return Poly(*this)%=r;}
	Poly dif()const{
		assert(size());
		if(size()==1){
			return {0};
		}else{
			Poly r(size()-1);
			rep(i,r.size())
				r[i]=(*this)[i+1]*(i+1);
			return r;
		}
	}
	Poly inte(const mint invs[])const{
		Poly r(size()+1,0);
		rep(i,size())
			r[i+1]=(*this)[i]*invs[i+1];
		return r;
	}
	//VERIFY: yosupo
	//opencupXIII GP of Peterhof H
	Poly log(int s,const mint invs[])const{
		assert((*this)[0]==1);
		if(s==1)return {0};
		return (low(s).dif()*inv(s-1)).low(s-1).inte(invs);
	}
	//Petrozavodsk 2019w mintay1 G
	//yosupo judge
	//UOJ Round23 C
	Poly exp(int s,const mint invs[])const{
		assert((*this)[0]==mint(0));
		Poly f{1},g{1};
		for(int n=1;;n*=2){
			if(n>=s)break;
			g=g*2-(g.square()*f).low(n);
			//if(n>=s)break;
			Poly q=low(n).dif();
			q=q+g*(f.dif()-f*q).low(2*n-1);
			f=f+(f*(low(2*n)-q.inte(invs))).low(2*n);
		}
		return f.low(s);
	}
	//exp(x),exp(-x) のペアを返す
	//UOJ Round23 C
	pair<Poly,Poly> exp2(int s,const mint invs[])const{
		assert((*this)[0]==mint(0));
		Poly f{1},g{1};
		for(int n=1;;n*=2){
			//if(n>=s)break;
			g=g*2-(g.square()*f).low(n);
			if(n>=s)break;
			Poly q=low(n).dif();
			q=q+g*(f.dif()-f*q).low(2*n-1);
			f=f+(f*(low(2*n)-q.inte(invs))).low(2*n);
		}
		return make_pair(f.low(s),g.low(s));
	}
	#ifndef USE_GOOD_MOD
	//CF250 E
	Poly sqrt(int s)const{
		assert((*this)[0]==1);
		static const mint half=mint(1)/mint(2);
		Poly r{1};
		for(int n=1;n<s;n*=2)
			r=(r+(r.inv(n*2)*low(n*2)).low(n*2))*half;
		return r.low(s);
	}
	#else
	//11/6
	//VERIFY: yosupo
	Poly sqrt(int s)const{
		assert((*this)[0]==1);
		static const mint half=mint(1)/mint(2);
		vc<mint> f{1},g{1},z{1};
		for(int n=1;n<s;n*=2){
			rep(i,n)z[i]*=z[i];
			inplace_fmt(z,true);
			
			vc<mint> delta(2*n);
			rep(i,n)delta[n+i]=z[i]-freq(i)-freq(n+i);
			inplace_fmt(delta,false);
			
			vc<mint> gbuf(2*n);
			rep(i,n)gbuf[i]=g[i];
			inplace_fmt(gbuf,false);
			
			rep(i,2*n)delta[i]*=gbuf[i];
			inplace_fmt(delta,true);
			f.resize(2*n);
			rng(i,n,2*n)f[i]=-half*delta[i];
			
			if(2*n>=s)break;
			
			z=f;
			inplace_fmt(z,false);
			
			vc<mint> eps=gbuf;
			rep(i,2*n)eps[i]*=z[i];
			inplace_fmt(eps,true);
			
			rep(i,n)eps[i]=0;
			inplace_fmt(eps,false);
			
			rep(i,2*n)eps[i]*=gbuf[i];
			inplace_fmt(eps,true);
			g.resize(2*n);
			rng(i,n,2*n)g[i]=-eps[i];
		}
		f.resize(s);
		return f;
	}
	#endif
	pair<Poly,Poly> divide(const Poly&r,const Poly&rri)const{
		Poly a=quotient(r,rri);
		Poly b=*this-a*r;
		return make_pair(a,b.low(r.size()-1));
	}
	//Yukicoder No.215
	Poly pow_mod(int n,const Poly&r)const{
		Poly rri=r.rev().inv(r.size());
		Poly cur{1},x=*this%r;
		while(n){
			if(n%2)
				cur=(cur*x).divide(r,rri).b;
			x=(x*x).divide(r,rri).b;
			n/=2;
		}
		return cur;
	}
	int lowzero()const{
		rep(i,size())if((*this)[i]!=0)return i;
		return size();
	}
	//VERIFY: yosupo
	//UOJ Round23 C (z=0,p<0)
	Poly pow(int s,int p,const mint invs[])const{
		assert(s>0);
		int n=size(),z=0;
		for(;z<n&&(*this)[z]==0;z++);
		assert(z==0||p>=0);
		if(z*p>=s)return Poly(s,0);
		mint c=(*this)[z],cinv=c.inv();
		mint d=c.pow(p);
		int t=s-z*p;
		Poly x(t);
		rng(i,z,min(z+t,n))x[i-z]=(*this)[i]*cinv;
		x=x.log(t,invs);
		rep(i,t)x[i]*=p;
		x=x.exp(t,invs);
		rep(i,t)x[i]*=d;
		Poly y(s);
		rep(i,t)y[z*p+i]=x[i];
		return y;
	}
	mint eval(mint x)const{
		mint r=0,w=1;
		for(auto v:*this){
			r+=w*v;
			w*=x;
		}
		return r;
	}
};

//CF641 F2
//f*x^(-a)
template<class mint>
struct Laurent{
	Poly<mint> f;
	int a;
	Laurent(const Poly<mint>&num,const Poly<mint>&den,int s){
		a=den.lowzero();
		assert(a<si(den));
		f=(num*(den>>a).inv(s)).low(s);
	}
	Laurent(const Poly<mint>&ff,int aa):f(ff),a(aa){}
	Laurent dif()const{
		return Laurent(f*(-a)+(f.dif()<<1),a+1);
	}
	mint&operator[](int i){
		assert(inc(0,i+a,si(f)-1));
		return f[i+a];
	}
};

template<class mint>
ll m2l(mint a){
	return a.v<mint::mod/2?a.v:ll(a.v)-ll(mint::mod);
}

template<class mint>
void showpoly(const Poly<mint>&a){
	vi tmp(si(a));
	rep(i,si(a)){
		tmp[i]=m2l(a[i]);
	}
	cerr<<tmp<<endl;
}


#ifndef DYNAMIC_MOD
extern constexpr modinfo base{998244353,3};
//extern constexpr modinfo base{1000000007,0};
//modinfo base{1,0};
#ifdef USE_GOOD_MOD
static_assert(base.mod==998244353);
#endif
#else
modinfo base(1,0);
extern constexpr modinfo base107(1000000007,0);
using mint107=modular<base107>;
#endif
using mint=modular<base>;

mint parity(int i){
	return i%2==0?1:-1;
}

#ifdef LOCAL
const int vmax=1010;
#else
const int vmax=(1<<21)+10;
#endif
mint fact[vmax],finv[vmax],invs[vmax];
void initfact(){
	fact[0]=1;
	rng(i,1,vmax){
		fact[i]=fact[i-1]*i;
	}
	finv[vmax-1]=fact[vmax-1].inv();
	for(int i=vmax-2;i>=0;i--){
		finv[i]=finv[i+1]*(i+1);
	}
	for(int i=vmax-1;i>=1;i--){
		invs[i]=finv[i]*fact[i-1];
	}
}
mint choose(int n,int k){
	return fact[n]*finv[n-k]*finv[k];
}
mint binom(int a,int b){
	return fact[a+b]*finv[a]*finv[b];
}
mint catalan(int n){
	return binom(n,n)-(n-1>=0?binom(n-1,n+1):0);
}

/*
const int vmax=110;
mint binbuf[vmax][vmax];
mint choose(int n,int k){
	return binbuf[n-k][k];
}
mint binom(int a,int b){
	return binbuf[a][b];
}
void initfact(){
	binbuf[0][0]=1;
	rep(i,vmax)rep(j,vmax){
		if(i)binbuf[i][j]+=binbuf[i-1][j];
		if(j)binbuf[i][j]+=binbuf[i][j-1];
	}
}
*/

mint p2[vmax],p2inv[vmax];
void initp2(){
	p2[0]=1;
	rep(i,vmax-1)p2[i+1]=p2[i]*2;
	p2inv[vmax-1]=p2[vmax-1].inv();
	per(i,vmax-1)p2inv[i]=p2inv[i+1]*2;
}

//verify yosupo
vc<mint> sampling_shift(vc<mint> a,mint c,int m){
	int n=si(a);
	rep(i,n)a[i]*=finv[i];
	vc<mint> b(finv,finv+n);
	rep(i,n)b[i]*=parity(i);
	chmult(a,b,n);
	rep(i,n)a[i]*=fact[i];
	reverse(all(a));
	mint w=1;
	rep(i,n){
		b[i]=finv[i]*w;
		w*=(c-i);
	}
	chmult(a,b,n);
	reverse(all(a));
	rep(i,n)a[i]*=finv[i];
	a.resize(m);
	b.resize(m);
	rep(i,m)b[i]=finv[i];
	chmult(a,b,m);
	rep(i,m)a[i]*=fact[i];
	return a;
}

void extend_poly(vc<mint>&a,int m){
	int n=si(a);
	rep(i,n)a[i]*=finv[i];
	vc<mint> b(finv,finv+n);
	rep(i,n)b[i]*=parity(i);
	chmult(a,b,n);
	a.resize(m);
	b.resize(m);
	rep(i,m)b[i]=finv[i];
	chmult(a,b,m);
	rep(i,m)a[i]*=fact[i];
}

void extend_polys(vvc<mint>&as,int m){
	int n=si(as[0]);
	for(auto&a:as)assert(si(a)==n);
	for(auto&a:as)rep(i,n)a[i]*=finv[i];
	vc<mint> b(finv,finv+n);
	rep(i,n)b[i]*=parity(i);
	for(auto&a:as)chmult(a,b,n);
	for(auto&a:as)a.resize(m);
	b.resize(m);
	rep(i,m)b[i]=finv[i];
	for(auto&a:as)chmult(a,b,m);
	for(auto&a:as)rep(i,m)a[i]*=fact[i];
}

struct large_factorial{
	int s;
	vc<mint> x;
	large_factorial():s(1),x(1,1){
		while(sq(s)<mint::mod-1){
			extend_poly(x,4*s);
			rep(i,2*s)x[i]=x[i*2]*(s*(2*i+1)+1)*x[i*2+1];
			x.resize(s*=2);
		}
		rep(i,s)x[i]*=i*s+1;
	}
	mint getfact(int i){
		int p=i/s;
		mint res=1;
		rep(j,p)res*=x[j];
		rng(j,p*s,i)res*=j+1;
		return res;
	}
};

//Codechef 2021 January Lunchtime EXPGROUP
//yosupo product of polynomial sequence
struct F{
	int n;
	vc<mint> rw,buf;
	static int getp2(int v){
		return 1<<(topbit(v-1)+1);
	}
	F():n(0){}
	F(const vc<mint>&given):rw(given){
		n=si(rw);
		assert(n>0);
	}
	F(initializer_list<mint> init):rw(all(init)){
		n=si(rw);
		assert(n>0);
	}
	int size()const{return n;}
	bool empty()const{return n==0;}
	void assume_have(){
		if(rw.empty()){
			int s=getp2(n);
			assert(si(buf)>=s);
			rw.resize(s);
			rep(i,s)rw[i]=buf[i].v;
			inplace_fmt(rw,true);
			rw.resize(n);
		}
		assert(si(rw)==n);
	}
	vc<mint> getrw(){
		assume_have();
		return rw;
	}
	void prepare(int len){
		if(si(buf)<len)assume_have();
		if(buf.empty()){
			int s=getp2(n);
			buf.resize(s);
			rep(i,n)buf[i]=rw[i];
			inplace_fmt(buf,false);
		}
		while(si(buf)<len){
			int s=si(buf);
			buf.resize(s*2);
			rep(i,n)buf[s+i]=rw[i];
			half_fmt(s,buf.data()+s);
		}
	}
	void copy_from(F&a){
		n=a.n;
		rw=a.rw;
		if(si(a.buf)){
			int s=getp2(n);
			buf.resize(s);
			rep(i,s)buf[i]=a.buf[i];
		}else buf.clear();
	}
	void init_from_sum(F&a,F&b){
		if(a.empty())return copy_from(b);
		if(b.empty())return copy_from(a);
		n=max(a.n,b.n);
		if(si(a.rw)&&si(b.rw)){
			rw.resize(n);
			rep(i,n){
				rw[i]=0;
				if(i<a.n)rw[i]+=a.rw[i];
				if(i<b.n)rw[i]+=b.rw[i];
			}
		}else rw.clear();
		int s=getp2(n);
		if(si(a.buf)>=s&&si(b.buf)>=s){
			buf.resize(s);
			rep(i,s)buf[i]=mint(a.buf[i].v)+mint(b.buf[i].v);
		}else buf.clear();
		if(rw.empty()&&buf.empty()){
			a.prepare(n);
			b.prepare(n);
			buf.resize(s);
			rep(i,s)buf[i]=mint(a.buf[i].v)+mint(b.buf[i].v);
		}
	}
	void init_from_product(F&a,F&b){
		assert(a.n>0);
		assert(b.n>0);
		n=a.n+b.n-1;
		rw.clear();
		int s=getp2(n);
		a.prepare(n);
		b.prepare(n);
		buf.resize(s);
		rep(i,s)buf[i]=a.buf[i]*b.buf[i];
	}
	F operator*(F&b){
		F res;
		res.init_from_product(*this,b);
		return res;
	}
	F operator+(F&b){
		F res;
		res.init_from_sum(*this,b);
		return res;
	}
	F operator+(F&&b){
		F res;
		res.init_from_sum(*this,b);
		return res;
	}
	F& operator*=(F&b){
		return *this=(*this)*b;
	}
	F& operator+=(F&b){
		return *this=(*this)+b;
	}
	F& operator+=(F&&b){
		return *this=(*this)+b;
	}
};
//転置原理
//a,b: x の多項式
//n=deg(a),m=deg(b)
//a*b の各係数に何かをかけたものが答え（に寄与），という状況があったとする
//これは適当な関数 c があって，ans+=[x^{n+m}] a*b*c という風に書ける
//b が入力で固定されているならば，deg(d)=n なる多項式 d であって，
//ans+=[x^n] a*d となるものがある
//そのような d を持ってくる
F middle(F&b,F&c){
	int m=si(b)-1,nm=si(c)-1,n=nm-m;
	assert(n>=0);
	int s=F::getp2(nm+1);
	b.prepare(s);
	c.prepare(s);
	static vc<mint> buf;
	buf.resize(s);
	rep(i,s)buf[i]=b.buf[i]*c.buf[i];
	inplace_fmt(buf,true);
	rep(i,n+1)buf[i]=buf[i+m];
	buf.resize(n+1);
	return F(buf);
}

void slv1(int t){
	using V=array<F,2>;
	using M=array<V,2>;
	
	int kmax=0;
	vc<pi> nk(t);
	for(auto&[n,k]:nk){
		cin>>n>>k;
		n%=mint::mod;
		chmax(kmax,k);
	}
	vc<pi> qs;
	rep(i,kmax)qs.eb(i,inf);
	rep(i,t)qs.eb(nk[i].b,i);
	sort(all(qs));
	
	int s=si(qs);
	
	using T=tuple<M,F>;
	vc<T> buf(2*s);
	auto getid=[&](int l,int r){
		if(r-l==1)return l+r;
		else return (l+r)/2*2;
	};
	{
		auto dfs=[&](auto self,int l,int r)->void{
			auto&[a,b]=buf[getid(l,r)];
			if(r-l==1){
				if(qs[l].b<inf){
					mint x=nk[qs[l].b].a;
					a[0][0]={1,-x};
					a[0][1]={0,0};
					a[1][0]={0,0};
					a[1][1]={1,-x};
					b={1,-x};
				}else{
					int i=qs[l].a;
					a[0][0]={2,-2*i};
					a[0][1]={i,-i*(i-1)/2};
					a[1][0]={0,1};
					a[1][1]={0,0};
					b={0,1};
				}
			}else{
				int m=(l+r)/2;
				self(self,l,m);
				self(self,m,r);
				auto&[al,bl]=buf[getid(l,m)];
				auto&[ar,br]=buf[getid(m,r)];
				rep(i,2)rep(j,2)rep(k,2)
					a[i][k]+=ar[i][j]*al[j][k];
				b=br*bl;
			}
		};
		dfs(dfs,0,s);
	}
	V ini;
	{
		auto&[a,b]=buf[getid(0,s)];
		Poly<mint> rw=b.getrw();
		rw.erase(rw.bg,rw.bg+kmax);
		rw=rw.inv(kmax+1);
		rw.resize(s);
		rotate(rw.bg,rw.bg+kmax+1,rw.ed);
		ini[0]=rw;
		ini[1]=vc<mint>(s);
	}
	vc<mint> ans(t);
	{
		auto dfs=[&](auto self,int l,int r,V z)->void{
			rep(k,2)assert(si(z[k])==r-l);
			if(r-l==1){
				mint val=z[0].getrw()[0];
				if(qs[l].b<inf)ans[qs[l].b]=val;
			}else{
				int m=(l+r)/2;
				auto&[al,bl]=buf[getid(l,m)];
				auto&[ar,br]=buf[getid(m,r)];
				
				V zl,zr;
				rep(i,2)zl[i]=middle(br,z[i]);
				rep(i,2)rep(j,2)zr[i]+=middle(al[i][j],z[j]);
				
				self(self,l,m,zl);
				self(self,m,r,zr);
			}
		};
		dfs(dfs,0,s,ini);
	}
	rep(i,t)print(ans[i]);
}

void slv2(){
	int n,k;cin>>n>>k;
	if(k>=mint::mod)return print(0);
	n%=mint::mod;
	
	vvc<mint> a(4);
	rep(i,3){
		a[0].pb(2*n-2*i);
		a[1].pb((n-(i-1)*invs[2])*i);
		a[2].pb(1);
		a[3].pb(0);
	}
	int s=1;
	while(s*(2*s+1)<k){
		extend_polys(a,8*s+2);
		rep(i,4*s+1){
			mint v[2][2];
			rep(x,2)rep(y,2)rep(z,2)
				v[x][z]+=a[x*2+y][i*2+1]*a[y*2+z][i*2];
			rep(x,2)rep(y,2)
				a[x*2+y][i]=v[x][y];
		}
		rep(j,4)a[j].resize(4*s+1);
		s*=2;
	}
	int p=k/s;
	mint v[2]{1,0};
	rep(i,p){
		mint w[2];
		rep(x,2)rep(y,2)
			w[x]+=a[x*2+y][i]*v[y];
		swap(v,w);
	}
	rng(i,p*s,k){
		mint tmp=v[0];
		v[0]=(2*n-2*i)*v[0]+(n-(i-1)*invs[2])*i*v[1];
		v[1]=tmp;
	}
	print(v[0]);
}

signed main(){
	cin.tie(0);
	ios::sync_with_stdio(0);
	cout<<fixed<<setprecision(20);
	
	initfact();
	int t;cin>>t;
	if(t<=5){rep(_,t)slv2();}
	else{slv1(t);}
}