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| #include<cstdio> #include<cstring> #include<algorithm> #include<iostream> #include<queue> #include<map> #include<stack> #include<cmath> #include<set> #include<bitset> #include<complex> #include<cstdlib> #include<assert.h> #define inc(i,l,r) for(int i=l;i<=r;i++) #define dec(i,l,r) for(int i=l;i>=r;i--) #define link(x) for(edge *j=h[x];j;j=j->next) #define mem(a) memset(a,0,sizeof(a)) #define ll long long #define eps 1e-8 #define succ(x) (1<<x) #define lowbit(x) (x&(-x)) #define mid (x+y>>1) #define sqr(x) ((x)*(x)) #define NM 140005 #define nm 400005 using namespace std; const double pi=acos(-1); const ll inf=998244353; ll read(){ ll x=0,f=1;char ch=getchar(); while(!isdigit(ch)){if(ch=='-')f=-1;ch=getchar();} while(isdigit(ch))x=x*10+ch-'0',ch=getchar(); return f*x; }
inline void reduce(ll&x){x+=x>>63&inf;} inline ll qpow(ll x,ll t){ ll s=1; for(;t;t>>=1,x=x*x%inf)if(t&1)s=s*x%inf; return s; }
namespace Poly{ int lim,bit,rev[NM],w[NM],W[NM]; ll invn; void clear(ll*a,ll*b){if(a<b)memset(a,0,sizeof(ll)*(b-a));} void init(int m){ for(lim=1,bit=0;lim<m;lim<<=1)bit++;invn=qpow(lim,inf-2); inc(i,1,lim-1)rev[i]=(rev[i>>1]>>1)|((i&1)<<(bit-1)); ll t=qpow(3,(inf-1)/lim);W[0]=1; inc(i,1,lim)W[i]=W[i-1]*t%inf; } void fft(ll*a,int f=0){ int n=lim; inc(i,1,n-1)if(i<rev[i])swap(a[i],a[rev[i]]); for(int k=1;k<n;k<<=1){ int t=n/k>>1; for(int i=0,j=0;i<k;i++,j+=t)w[i]=W[f?n-j:j]; for(int i=0;i<n;i+=k<<1) for(int j=0;j<k;j++){ ll x=a[i+j],y=w[j]*a[i+j+k]%inf; reduce(a[i+j]=x+y-inf);reduce(a[i+j+k]=x-y); } } if(f)inc(i,0,n-1)a[i]=a[i]*invn%inf; } ll _a[NM]; void inv(ll*b,ll*a,int m){ if(m==1){b[0]=qpow(a[0],inf-2);return;} inv(b,a,m+1>>1);init(m<<1); copy(a,a+m,_a);clear(_a+m,_a+lim);clear(b+m,b+lim); fft(b);fft(_a); inc(i,0,lim-1)b[i]=b[i]*(2-_a[i]*b[i]%inf+inf)%inf; fft(b,1);clear(b+m,b+lim); } ll _b[NM]; void div(ll*c,ll*d,ll*a,ll*b,int n,int m){ reverse_copy(a,a+n,c);reverse_copy(b,b+m,d); inv(_b,d,n-m+1);reverse(d,d+m); init(n-m+1<<1);clear(c+n-m+1,c+lim); fft(_b);fft(c); inc(i,0,lim-1)c[i]=c[i]*_b[i]%inf; fft(c,1); reverse(c,c+n-m+1);clear(c+n-m+1,c+lim); init(n); copy(c,c+n-m+1,_b);clear(_b+n-m+1,_b+lim); m--;clear(d+m,d+lim); fft(_b);fft(d); inc(i,0,lim-1)d[i]=d[i]*_b[i]%inf; fft(d,1); clear(d+m,d+lim);clear(_b,_b+lim); inc(i,0,m-1)reduce(d[i]=a[i]-d[i]); } vector<ll>p[NM],q[NM];ll _c[NM]; void build(int i,int x,int y,const ll*a){ if(x==y){p[i].clear();p[i].push_back(inf-a[x]);p[i].push_back(1);return;} build(i<<1,x,mid,a);build(i<<1|1,mid+1,y,a); int n=p[i<<1].size(),m=p[i<<1|1].size(); init(n+m-1); copy(p[i<<1].begin(),p[i<<1].end(),_a);clear(_a+n,_a+lim); copy(p[i<<1|1].begin(),p[i<<1|1].end(),_b);clear(_b+m,_b+lim); fft(_a);fft(_b); inc(j,0,lim-1)_c[j]=_a[j]*_b[j]%inf; fft(_c,1);p[i].assign(_c,_c+n+m-1); } ll _d[NM],tmp[NM],ret[NM]; void DIV(int x,int y){ if(q[x].size()<p[y].size()){q[y]=q[x];return;} copy(q[x].begin(),q[x].end(),_c);copy(p[y].begin(),p[y].end(),_d); div(tmp,ret,_c,_d,q[x].size(),p[y].size()); q[y].assign(ret,ret+p[y].size()-1); while(!q[y].back())q[y].pop_back(); } void cal(int i,int x,int y,ll*a){ if(x==y){a[x]=q[i][0];return;} DIV(i,i<<1);DIV(i,i<<1|1); cal(i<<1,x,mid,a);cal(i<<1|1,mid+1,y,a); } void out(ll*a,int m){inc(i,0,m-1)printf("%lld%c",a[i]," \n"[i==m-1]);} }
int n,m; ll _x,_y,_t; ll inv[NM],invp[NM],p[NM]; ll b[NM],c[NM],st[NM],a[NM],ans[NM];
void init(){ inc(i,0,n)if(i&1)a[i]=inf-invp[i];else a[i]=invp[i]; inc(i,0,n)st[i]=qpow(i,n)*invp[i]%inf; Poly::init(n<<1|1); Poly::clear(a+n+1,a+Poly::lim); Poly::clear(st+n+1,st+Poly::lim); Poly::fft(a);Poly::fft(st); inc(i,0,Poly::lim-1)st[i]=st[i]*a[i]%inf; Poly::fft(st,1); }
int main(){ n=5e4;p[0]=p[1]=inv[1]=invp[0]=invp[1]=1; inc(i,2,n)p[i]=p[i-1]*i%inf,inv[i]=inv[inf%i]*(inf-inf/i)%inf,invp[i]=invp[i-1]*inv[i]%inf; while(~scanf("%d%d",&n,&m)){ inc(i,1,m){ reduce(_x=read()%inf);reduce(_y=read()%inf);reduce(_t=read()%inf);read(); b[i]=qpow(_t+1,inf-2); c[i]=qpow(_x,n)*_y%inf*b[i]%inf*invp[n]%inf; } init(); inc(i,0,n)if(i&1)a[i]=inf-st[i]*p[i]%inf;else a[i]=st[i]*p[i]%inf; Poly::build(1,1,m,b); Poly::q[0].assign(a,a+n+1); Poly::DIV(0,1); Poly::cal(1,1,m,ans); inc(i,1,m)ans[i]=ans[i]*c[i]%inf; inc(i,1,m)if(b[i]==1){ if(n&1)printf("%lld\n",(inf-c[i])%inf); else printf("%lld\n",c[i]); }else if(b[i]==0)printf("-1\n"); else printf("%lld\n",ans[i]); } return 0; }
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