#include <bits/stdc++.h>
#pragma GCC optimize("O3,unroll-loops")
#define pb push_back
#define F first
#define S second
#define ld long double
#define all(a) a.begin(),a.end()
#define pii pair <int,int>
#define ll long long
#define PII pair<pii , pii>
#define sz(v) (int)v.size()
#define rep(i , a , b) for(int i=a;i <= (b);i++)
#define per(i , a , b) for(int i=a;i >= (b);i--)
#define deb(x) cout <<#x << " : " << x << "\n" ;
using namespace std ;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
const ll maxn = 1e8+10 + 10, inf = 1e9+10 , mod = 1e9 + 7 ;
int a2[maxn] ;
ll dp[62][62][122] , pr[130] ;
ll po(ll a,ll b){
if(b==0)return 1 ;
ll v =po(a,b/2);
v=v *v % mod ;
if(b&1) v= v*a % mod;
return v;
}
ll ch(ll x ,ll d , ll k){
if(d==-1)return 0;
d = min(d , k-x);
return ((1ll<<(d+1))-1);
}
ll ans =0 , N , d[130] ;
vector <ll> cal(ll p){
ll x = p , k= 0 ;
vector <ll> h;
while(x*2 <= N){
x *= 2 ;
k++;
}
rep(i , 0 , k)h.pb((1ll<<i)) ;
if((x+(1ll<<k)-1) <= N){
return h ;
}
ll az = (x+(1ll<<k)-1) - N ;
h.back()-=az;
return h ;
}
void f(ll p = 1){
if(p > N)return ;
ll x= p , k =0 ;
while(x*2 <= N){
k++;
x*=2 ;
}
if((x+(1ll<<k)-1) <= N){
pr[0] = 0 ;
rep(i , 1 ,120)pr[i] = pr[i-1] + d[i] ;
rep(i , 0 , k){
ll sm = 0 ;
rep(j , 0 , 120){
ll t = dp[k][i][j] + (j >= i ? pr[j-i] : 0);
if(t == N)break ;
sm = (sm + po2((N-t)%(mod-1))-1);
if(sm > mod)sm -= mod ;
}
sm += mod;
if(sm > mod)sm-=mod;
ans = (ans + sm*po2(i))%mod ;
}
return ;
}
vector <ll> A = cal(p*2) ;
vector <ll> B = cal(p*2+1) ;
ll d2[130] , ls[130] ;
rep(i , 0 , 120){
d2[i] =0 ;
ls[i] = d[i] ;
}
d2[1] = 1 ;
rep(i , 1 , 120){
d2[i] += d[i-1] ;
}
rep(i , 0 , sz(B)-1){
d2[i+2] += B[i] ;
}
rep(i , 0 , 120){
swap(d[i] , d2[i]) ;
}
f(p*2) ;
rep(i , 0 , sz(B)-1){
d[i+2] -= B[i] ;
}
rep(i , 0 ,sz(A)-1){
d[i+2] += A[i] ;
}
f(p*2+1);
rep(i , 0 , 120)d[i] = ls[i] ;
pr[0] = d[0] ;
rep(i , 1, 120)pr[i] = pr[i-1] + d[i] ;
rep(i , 1 , sz(A)-1)A[i] += A[i-1] ;
rep(i , 1, sz(B)-1)B[i] += B[i-1] ;
rep(i , 0 , 120){
if(i ==0){
ans = (ans + po2((N-1)%(mod-1))-1);
if(ans > mod)ans-=mod;
continue ;
}
ll t = pr[i] + A[min(sz(A)-1 , i-1)] + B[min(sz(B)-1 , i-1)]+1 ;
if(t==N)break ;
ans = (ans + po2((N-t)%(mod-1))-1);
if(ans > mod)ans -= mod ;
}
}
signed main(){
ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
a2[0] = 1;
rep(i , 1 ,maxn-1){
a2[i] = (1ll*a2[i-1]*2ll%mod) ;
}
rep(k , 0 , 60){
rep(i , 0 , k){
rep(d , 0 , 120){
ll ans = ch(i , d , k) ;
ll x = i-1 , D = d-1 ;
while(x!=-1 && D!=-1){
ans++ ;
ans = (ans + ch(x+1 , D-1 , k));
D--;
x--;
}
dp[k][i][d] = ans ;
}
}
}
map <ll,ll> mp ;
int T ;
cin >> T ;
while(T--){
rep(i ,0 , 120)d[i] =0 ;
ll n;
cin >> n ;
if(mp[n]!=0){
cout << mp[n] << "\n";
continue ;
}
N = n ;
ans =0 ;
f();
mp[n] = ans * po(po(2,n)-1 , mod-2)%mod;
cout << ans * po(po(2,n)-1 , mod-2)%mod << "\n";
}
return 0 ;
}
/*
*/
Compilation message
Main.cpp: In function 'void f(long long int)':
Main.cpp:68:28: error: 'po2' was not declared in this scope; did you mean 'po'?
68 | sm = (sm + po2((N-t)%(mod-1))-1);
| ^~~
| po
Main.cpp:73:29: error: 'po2' was not declared in this scope; did you mean 'po'?
73 | ans = (ans + sm*po2(i))%mod ;
| ^~~
| po
Main.cpp:109:26: error: 'po2' was not declared in this scope; did you mean 'po'?
109 | ans = (ans + po2((N-1)%(mod-1))-1);
| ^~~
| po
Main.cpp:115:22: error: 'po2' was not declared in this scope; did you mean 'po'?
115 | ans = (ans + po2((N-t)%(mod-1))-1);
| ^~~
| po
