#include <bits/stdc++.h> #define ll long long #define fi first #define se second #define pb push_back #define ii pair<ll, ll> #define all(a) a.begin(), a.end() #define iii pair<ii, ll> #define ld long double using namespace std; const ll N = 2e2+5; const ll mod = 1e9+7; const ll inf=4e18+3; const ll lg =18; ll n,i,j,m,q,k,t; ll x,y; ll a[N],f[N],r[N]; ll mu(ll a,ll b) { if(b==0) return 1; if(b==1) return a%mod; ll res=mu(a,b/2); res=res*res%mod; if(b&1) res=res*a%mod; return res; } vector<ll>ans={0,666666672,571428577,733333341,548387104,285714292,401574811,54901967,305283766,687194538,930630205,637851051,269564167,48220727,68575102,889417886,481716032,687056319,954051904,121547830,239217412,999114059,498264988,847103550,758761690,638522568,268899203,802375319,911887665,665647523,347470132,249948686,415505300,293580916,631099079,133397470,179641631,908225308,735415978,370496430,925361906,675702668,992844490,586790472,486337579,425150383,664592138,914789996,772456654,799879782,899195971,337434977,870849620,429060808,261158658,304825485,495778058,172841730,550803456,621379872,825247430,195174391,149707164,550237255,434017081,508502652,962252350,486033940,216956820,610127529,961466989,549906267,367921647,594964096,276698183,809717020,81528533,744656687,495311643,866954358,131441158,314370724,170132716,983933855,527513392,632834937,675660064,315749494,839731414,530949465,942829728,529725350,821306848,967466098,781228030,679039065,653977477,841867588,406101445,671916196,154660144,128303839,221224696,920685660,777084320,395430897,335136412,722644706,248891204,504457951,775248161,349796576,74857969,729964279,978279169,389616934,164479112,89793646,423460149,696236474,176676045,186090600,893614131,639796232,446656698,526261967,295038330,825220882,697866216,976082617,768952803,186815674,165986386,93773490,612773827,898380343,97082244,510520259,874516626,157110604,717223381,49756112,567353074,424486813,131235898,255307387,787070716,98378846,995605722,755309723,411918937,600100782,17321362,303222205,499750831,997171493,175600679,674410914,278528097,212497643,589944900,543573141,930376920,689938960,112006801,328572912,195606533,586277662,109153634,745980494,286667447,755139031,497350598,608913514,639723549,304170631,759757033,773061231,904529395,143673214,767943674,612568341,523953553,447605849,799432615,627312407,187297556,821063613,794958645,872059132,108593592,610831908,75896678,83678274,526936897,632317225,178730200,941861036,866083134,463189473}; vector<ll>ans2 ={0,0,571428577,401574811,68575102,347470132,149707164,295038330,246944817,168459846,848759170,753916649,874259235,436845857,455803345,732110426,912252260,380931639,725126576,755085026,497747095,601032270,132018618,195747679,326166778,90750519,950969612,561147124,716973945,398359507,245333203,645374876,58517764,882537570,387870120,174478760,770163916,657328870,392199940,752435265,596273060,880391751,607922078,465118232,314990412,429160328,670114601,83625202,713881005,807523234,400261067,826581252,770146593,608067344,280418783,20107917,573628670,767615667,381834390,980680016}; int main() { ios_base::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr); cin>>q; while(q--) { cin>>n; if(n<=200) cout<<ans[n-1]%mod<<'\n'; else{ ll k=__lg(n+1); cout<<ans2[k]<<'\n'; } /// n=2^k-1 } return 0; } /* (2^d-1)*(2^k) / (2^n-1) 2^d+k-n - 2^k-n */