#include<bits/stdc++.h>
using namespace std;
#define int long long
const int mod=1e9+7;
int n,m,ans,pw[35],T;
map<int,int>f[2][2],vis[2][2];
int Pow(int x,int y){
    int res=1;
    while(y){
        if(y&1){
            res=res*x%mod;
        }
        y=y/2;x=x*x%mod;
    }return res;
}
int get(int x){
    int res,o;
    for(int i=1;i<=31;i++){
        if(pw[i]-1<=x)o=i;
    }
    //cout<<x<<" "<<o<<" "<<pw[o]-1<<endl;
    int u=pw[o-1]-1;
    res=x-(pw[o]-1);
    res=min(res,pw[o-1]);
    res+=u;
    return res;
}
int dfs(int x,int y,int z){
    if(x==0)return 1;
    if(x==1){
        if(y==1&&z==0)return 0;
        return 1;
    }
    if(vis[y][z][x]==1)return f[y][z][x];
    int l1=get(x);
    int l2=x-1-l1;
    //cout<<x<<" "<<l1<<" "<<l2<<endl;
    vis[y][z][x]=1;
    int t;
    if(y==0&&z==0){
        t=dfs(l1,0,0)*dfs(l2,0,0)%mod*Pow(x,mod-2)%mod;
    }
    if(y==1&&z==1){
        t=dfs(l1,0,0)*dfs(l2,0,0)%mod;
    }
    if(y==1&&z==0){
        int p=2*l1*l2;p=p%mod;


        t=   dfs(l1,0,0)*dfs(l2,1,0)%mod*Pow(x-1,mod-2)%mod*l1%mod*(l2-1)%mod*Pow(p,mod-2)%mod;
        
        t=(t+dfs(l1,1,0)*dfs(l2,0,0)%mod*Pow(x-1,mod-2)%mod*l2%mod*(l1-1)%mod*Pow(p,mod-2))%mod;
        //cout<<t<<" "<<p<<" "<<Pow(12,mod-2)<<endl;



        t=(t+dfs(l1,0,0)*dfs(l2,1,1)%mod*Pow(l1+1,mod-2)%mod*(l1)%mod*Pow(p,mod-2))%mod;

        t=(t+dfs(l1,1,1)*dfs(l2,0,0)%mod*Pow(l2+1,mod-2)%mod*(l2)%mod*Pow(p,mod-2))%mod;
        
    }
    f[y][z][x]=t;
    cout<<f[y][z][x]<<" "<<x<<" "<<y<<" "<<z<<" "<<l1<<" "<<l2<<endl;
    return f[y][z][x];
}
signed main(){
    cin>>T;
    pw[0]=1;cout<<3*Pow(8,mod-2)%mod<<endl;
    for(int i=1;i<=31;i++)pw[i]=pw[i-1]*2;
    //cout<<get(3);return 0;
    vis[1][1][2]=1;
    vis[0][0][2]=1;
    vis[1][0][2]=1;
    f[1][1][2]=1;
    f[0][0][2]=Pow(2,mod-2);
    f[1][0][2]=1;
    while(T--){
        cin>>n;
        ans=(dfs(n,1,0)*(n-1)+dfs(n,1,1))%mod*Pow(n,mod-2)%mod;
        cout<<ans<<endl;
    }
}