hdu5829

  1 #include<iostream>
  2 #include<cstdio>
  3 #include<cmath>
  4 #include<cstring>
  5 #include<algorithm>
  6 typedef long long ll;
  7 using namespace std;
  8 const int mo=998244353;
  9 const int g=3;
 10 int e[100010],a[100000*4],b[100010*4],jc[100010],d[100010],ni[100010],r[100010*4];
 11 int w[30][2],ans[100010],rg[30];
 12 int cas,m,n;
 13 bool cmp(int a,int b)
 14 {
 15   return a>b;
 16 }
 17 
 18 ll quick(ll x,int y)
 19 {
 20   ll s=1;
 21   while (y)
 22   {
 23     if (y&1) s=s*x%mo;
 24     x=x*x%mo; y>>=1;
 25   }
 26   return s;
 27 }
 28 void ntt(int *a, int f)
 29 {
 30   for (int i=0; i<n; i++)
 31     if (i<r[i]) swap(a[i],a[r[i]]);
 32   int now=0;
 33   for (int i=1; i<n; i<<=1)
 34   {
 35     int p=w[++now][f];
 36     for (int j=0; j<n; j+=i<<1)
 37     {
 38       int w=1;
 39       for (int k=0; k<i; k++)
 40       {
 41          int u=a[k+j],v=1ll*w*a[j+k+i]%mo;
 42          a[j+k]=(u+v)%mo;
 43          a[j+k+i]=(u-v+mo)%mo;
 44          w=1ll*w*p%mo;
 45       }
 46     }
 47   }
 48 }
 49 
 50 int main()
 51 {
 52   freopen("1.in","r",stdin);
 53   int now=(mo-1)/2,ng=quick(g,mo-2),l=0;
 54   while (now%2==0)
 55   {
 56     w[++l][1]=quick(g,now);
 57     w[l][0]=quick(ng,now);
 58     rg[l]=quick(1<<l,mo-2);
 59     now>>=1;
 60   }
 61   jc[0]=d[0]=ni[0]=1;
 62   for (int i=1; i<=100000; i++)
 63   {
 64     jc[i]=1ll*jc[i-1]*i%mo;
 65     ni[i]=quick(jc[i],mo-2);
 66     d[i]=2*d[i-1]%mo;
 67   }
 68   scanf("%d",&cas);
 69   while (cas--)
 70   {
 71     scanf("%d",&m);
 72     for (int i=1; i<=m; i++)
 73       scanf("%d",&e[i]);
 74     sort(e+1,e+1+m,cmp);
 75     memset(a,0,sizeof(a));
 76     memset(b,0,sizeof(b));
 77     for (int i=1; i<=m; i++)
 78       a[i]=1ll*jc[i-1]*d[m-i]%mo*e[i]%mo;
 79     for (int i=0; i<=m; i++)
 80       b[m-i]=ni[i];
 81    /* for (int i=m+1; i<2*m+1; i++)
 82     {
 83       int s=0;
 84       for (int j=0; j<=i; j++) s=(s+1ll*a[j]*b[i-j]%mo)%mo;
 85       cout <<1ll*s*ni[i-m-1]%mo<<" ";
 86     }
 87     cout <<endl;
 88     break;*/
 89     int l=0;
 90     for (n=1; n<=2*m+1; n<<=1) l++;
 91     for (int i=0; i<n; i++) r[i]=(r[i>>1]>>1)|((i&1)<<(l-1));
 92     ntt(a,1); ntt(b,1);
 93     for (int i=0; i<n; i++) a[i]=1ll*a[i]*b[i]%mo;
 94     ntt(a,0);
 95     for (int i=m+1; i<2*m+1; i++)
 96       ans[i-m]=1ll*a[i]*ni[i-m-1]%mo*rg[l]%mo;
 97     for (int i=1; i<=m; i++)
 98       ans[i]=(ans[i-1]+ans[i])%mo;
 99     for (int i=1; i<=m; i++)
100       printf("%d ",ans[i]);
101     cout <<endl;
102   }
103   return 0;
104 }