SUBSFREQ.cpp

#include<bits/stdc++.h>
using namespace std;
using ll=long long ;
#define MOD 1000000007
ll fact[500005];
ll recpow(ll n,ll p ,ll m=MOD){
 ll ans=1;
 while(p)
 {
  if(p&1)ans=(ans*n)%m;
  n=(n*n)%m;
  p>>=1;
 }
 
 return ans%m;

}

ll mod_inv(ll n,ll m=MOD){
 return recpow(n,m-2,m);
}
ll nCr(ll n, ll r, ll m=MOD){
if(r==0)return 1;
return (((fact[n]*mod_inv(fact[n-r]))%m)*mod_inv(fact[r]))%m;
}

int main(){
ios_base::sync_with_stdio(false);
    cin.tie(NULL);
 int t;
 cin>>t;
 fact[0]=fact[1]=1;
 for(int i=2;i<500005;i++){
  fact[i]=(1ll*fact[i-1]*i)%MOD;
 }
 while(t--){
  ll n;
  cin>>n;
  ll a[n+1];
  map<ll,ll> mp;
  for(int i=0;i<n;i++){
   cin>>a[i];
   mp[a[i]]++;
  }
  ll cm[n+3],rem[n+1];
  for(int i=0;i<=n+1;i++){
          cm[i]=rem[i]=1;
  }

  for(auto x:mp)
  {
   ll sum=1;
   for(int j=1;j<=x.second;j++)
   {
                  sum+=nCr(x.second,j);
                  sum%=MOD;
                  cm[j]*=sum;
                  cm[j]%=MOD;        
   }
   rem[x.second+1]*=sum;
   rem[x.second+1]%=MOD;
  }

  ll mul=1;
  for(int i=1;i<=n;i++)
  {
          mul*=rem[i];
          mul%=MOD;
          cm[i]*=mul;
          cm[i]%=MOD;  
  }
  

  for(int i=1;i<=n;i++)
  { 
   ll res=0,ans,sum=1;
  

    for(int j=1;j<=mp[i];j++)
   {
    ll tmp;
              ans=nCr(mp[i],j);
                tmp=ans;
              sum+=ans;
              sum%=MOD;
              cm[j]=(cm[j]*mod_inv(sum))%MOD;
              ans*=cm[j];
              ans%=MOD;
              cm[j]=(cm[j]*(sum-tmp+MOD)%MOD)%MOD;
              res+=ans;
              res%=MOD;
             }
   


   cout<<res%MOD<<" ";
  }
  cout<<"\n";

  

 }
return 0;
}