#include using namespace std; typedef signed long long ll; #define _P(...) (void)printf(__VA_ARGS__) #define FOR(x,to) for(x=0;x<(to);x++) #define FORR(x,arr) for(auto& x:arr) #define FORR2(x,y,arr) for(auto& [x,y]:arr) #define ALL(a) (a.begin()),(a.end()) #define ZERO(a) memset(a,0,sizeof(a)) #define MINUS(a) memset(a,0xff,sizeof(a)) template bool chmax(T &a, const T &b) { if(a bool chmin(T &a, const T &b) { if(a>b){a=b;return 1;}return 0;} //------------------------------------------------------- int T; ll A,N; const ll mo=998244353; ll modpow(ll a, ll n = mo-2) { ll r=1;a%=mo; while(n) r=r*((n%2)?a:1)%mo,a=a*a%mo,n>>=1; return r; } template using vec=vector; //using vec=valarray; template vec fft(vec v, bool rev=false) { int n=v.size(),i,j,m; for(int m=n; m>=2; m/=2) { T wn=modpow(5,(mo-1)/m); if(rev) wn=modpow(wn); for(i=0;i=mo) v[j1]-=mo; w=(ll)w*wn%mo; } } } for(i=0,j=1;j>1;k>(i^=k);k>>=1); if(i>j) swap(v[i],v[j]); } if(rev) { ll rv = modpow(n); FOR(i,n) v[i]=(ll)v[i]*rv%mo; } return v; } template vec MultPoly(vec P,vec Q,bool resize=false) { if(resize) { int maxind=0,pi=0,qi=0,i; int s=2; FOR(i,P.size()) if(norm(P[i])) pi=i; FOR(i,Q.size()) if(norm(Q[i])) qi=i; maxind=pi+qi+1; while(s*2 R(s*2); for(int x=0;x<=pi;x++) for(int y=0;y<=qi;y++) (R[x+y]+=P[x]*Q[y])%=mo; return R; } vec P2(s*2),Q2(s*2); FOR(i,pi+1) P2[i]=P[i]; FOR(i,qi+1) Q2[i]=Q[i]; swap(P,P2),swap(Q,Q2); } P=fft(P), Q=fft(Q); for(int i=0;i vec AddPoly(vec P,vec Q) { if(P.size() vec SubPoly(vec P,vec Q) { if(P.size() vector inverse(vector a) { assert(a[0]>0); vector b={(T)modpow(a[0])}; while(b.size() c(a.begin(),a.begin()+min(a.size(),2*b.size())); vector d=MultPoly(b,b,true); if(d.size()>a.size()) d.resize(a.size()); c = MultPoly(c,d,true); b.resize(2*b.size()); int i; for(i=b.size()/2;i pair,vec> divmod(vec a,vec b) { //多項式除算。FPSには使えない。 //最高次数で反転する int A=-1,B=-1,i; FOR(i,a.size()) if(a[i]) A=i; FOR(i,b.size()) if(b[i]) B=i; assert(B>=0); if(A({0LL}),a); a.resize(A+1); b.resize(B+1); reverse(ALL(a)); reverse(ALL(b)); b.resize(A+1); auto rb=inverse(b); // 1/b rb.resize(A-B+1); auto c=MultPoly(a,rb,1); // c=a/b c.resize(A-B+1); reverse(ALL(c)); b.resize(B+1); reverse(ALL(b)); auto bc=MultPoly(c,b,1); //bc=a/b*b bc.resize(A+1); reverse(ALL(a)); auto r=SubPoly(a,bc); // r=a-bc r.resize(B); return make_pair(c,r); } vec multipoint_evaluation(vec f,vec m) { sort(ALL(m)); int ON=m.size(); //2の累乗にする while(m.size()&(m.size()-1)) m.push_back(m.back()+1); int i,N=m.size(); vec> Xs(2*N),Rs(2*N); FOR(i,N) { if(i=1;i--) Xs[i]=MultPoly(Xs[i*2],Xs[i*2+1],1); Rs[1]=divmod(f,Xs[1]).second; for(i=2;i<2*N;i++) { Rs[i]=divmod(Rs[i/2],Xs[i]).second; Rs[i].resize(Xs[i].size()-1); } vec ret; FOR(i,N) ret.push_back(Rs[N+i].empty()?0:Rs[N+i][0]); return ret; } void solve() { int i,j,k,l,r,x,y; string s; cin>>T; while(T--) { cin>>A>>N; ll S=floor(sqrt(N)); ll ret=0; for(i=S*S;i F,M; FOR(i,S) { F.push_back(modpow(A,1LL*S*S*i*i)); M.push_back(modpow(A,2*S*i)); } auto X=multipoint_evaluation(F,M); FOR(i,S) { (ret+=modpow(A,1LL*i*i)*X[i])%=mo; } cout<