#pragma GCC optimize("O3") #include using namespace std; #ifdef LOCAL #define _GLIBCXX_DEBUG #endif #pragma region Macros #define FOR(i, l, r) for(int i = (l) ;i < (r) ;i++) #define REP(i, n) FOR(i, 0, n) #define REPS(i, n) FOR(i, 1, n+1) #define RFOR(i, l, r) for(int i = (l) ; i >= (r) ; i--) #define RREP(i, n) RFOR(i, n - 1, 0) #define RREPS(i, n) RFOR(i, n , 1) #define SZ(x) ((int)(x).size()) #define all(x) (x).begin(), (x).end() #define rall(x) (x).rbegin(), (x).rend() template using V = vector; template using VV = V>; #define ll long long using ld = long double; #define pll pair #define pii pair #define pq priority_queue #define pb push_back #define eb emplace_back #define fi first #define se second #define endl '\n' #define ios ios_base::sync_with_stdio(0),cin.tie(0),cout.tie(0); #define lb(c,x) distance(c.begin(),lower_bound(all(c),x)) #define ub(c,x) distance(c.begin(),upper_bound(all(c),x)) #define VEC(type, name, size) \ V name(size); \ INPUT(name) #define VVEC(type, name, h, w) \ VV name(h, V(w)); \ INPUT(name) #define INT(...) \ int __VA_ARGS__; \ INPUT(__VA_ARGS__) #define LL(...) \ ll __VA_ARGS__; \ INPUT(__VA_ARGS__) #define STR(...) \ string __VA_ARGS__; \ INPUT(__VA_ARGS__) #define CHAR(...) \ char __VA_ARGS__; \ INPUT(__VA_ARGS__) #define DOUBLE(...) \ DOUBLE __VA_ARGS__; \ INPUT(__VA_ARGS__) #define LD(...) \ LD __VA_ARGS__; \ INPUT(__VA_ARGS__) void scan(int &a) { cin >> a;} void scan(long long &a) { cin >> a;} void scan(char &a) { cin >> a;} void scan(double &a) { cin >> a;} void scan(long double &a) { cin >> a;} void scan(char a[]) { scanf("%s", a);} void scan(string &a) { cin >> a;} template void scan(V &); template void scan(pair &); template void scan(V &a){ for(auto &i : a) scan(i); } template void scan(pair &p){ scan(p.first); scan(p.second); } template void scan(T &a) { cin >> a;} void INPUT() {} template void INPUT(Head &head, Tail &... tail){ scan(head); INPUT(tail...); } template inline void print(T x) { cout << x << '\n'; } template istream &operator>>(istream &is, pair &p) { is >> p.first >> p.second; return is; } template ostream &operator<<(ostream &os, const pair &p) { os << p.first << " " << p.second; return os; } template istream &operator>>(istream &is, vector &v) { for(T &in : v) is >> in; return is; } template ostream &operator<<(ostream &os, const V &v) { REP(i, SZ(v)) { if(i) os << " "; os << v[i]; } return os; } //debug template void view(const V &v) { cerr << "{ "; for(const auto &e : v) { cerr << e << ", "; } cerr << "\b\b }"; } template void view(const VV &vv) { cerr << "{\n"; for(const auto &v : vv) { cerr << "\t"; view(v); cerr << "\n"; } cerr << "}"; } template void view(const V> &v) { cerr << "{\n"; for(const auto &c : v) cerr << "\t(" << c.first << ", " << c.second << ")\n"; cerr << "}"; } template void view(const map &m) { cerr << "{\n"; for(auto &t : m) cerr << "\t[" << t.first << "] : " << t.second << "\n"; cerr << "}"; } template void view(const pair &p) { cerr << "(" << p.first << ", " << p.second << ")"; } template void view(const set &s) { cerr << "{ "; for(auto &t : s) { view(t); cerr << ", "; } cerr << "\b\b }"; } template void view(T e) { cerr << e; } #ifdef LOCAL void debug_out() {} template void debug_out(Head H, Tail... T) { view(H); cerr << ", "; debug_out(T...); } #define debug(...) \ do { \ cerr << __LINE__ << " [" << #__VA_ARGS__ << "] : ["; \ debug_out(__VA_ARGS__); \ cerr << "\b\b]\n"; \ } while(0) #else #define debug(...) (void(0)) #endif template V press(V &x) { V res = x; sort(all(res)); res.erase(unique(all(res)), res.end()); REP(i, SZ(x)) { x[i] = lower_bound(all(res), x[i]) - res.begin(); } return res; } template inline bool chmin(T &a, T b) { if(a > b) { a = b; return true; } return false; } template inline bool chmax(T &a, T b) { if(a < b) { a = b; return true; } return false; } inline void Yes(bool b = true) { cout << (b ? "Yes" : "No") << '\n'; } inline void YES(bool b = true) { cout << (b ? "YES" : "NO") << '\n'; } inline void err(bool b = true) { if(b) { cout << -1 << '\n'; exit(0); } } template inline void fin(bool b = true, T e = 0) { if(b) { cout << e << '\n'; exit(0); } } template T divup(T x, T y) { return (x + (y - 1)) / y; } template T pow(T a, long long n, T e = 1) { T ret = e; while(n) { if(n & 1) ret *= a; a *= a; n >>= 1; } return ret; } struct iofast { iofast() { ios_base::sync_with_stdio(false); cin.tie(nullptr); cout << fixed << setprecision(15); } } iofast_; const int inf = 1e9; const ll INF = 1e18; #pragma endregion inline int topbit(unsigned long long x){ return x?63-__builtin_clzll(x):-1; } inline int popcount(unsigned long long x){ return __builtin_popcountll(x); } inline int parity(unsigned long long x){//popcount%2 return __builtin_parity(x); } template T modpow(T base, T exp, T modulus) { base %= modulus; T result = 1; while (exp > 0) { if (exp & 1) result = (result * base) % modulus; base = (base * base) % modulus; exp >>= 1; } return result; } int main(){ LL(T); while(T--){ LL(N); N=2*N-1; ll val=N; V p; for(ll i=2;i*i<=val;i++){ if(val%i==0){ while(val%i==0){ val/=i; } p.push_back(i); } } if(val!=1) p.push_back(val); ll f=N; for(auto x:p){ f/=x; f*=x-1; } V q; for(ll i=1;i*i<=f;i++){ if(f%i==0){ q.push_back(i); if(i*i!=f) q.push_back(f/i); } } ll ans=INF; for(auto x:q){ ll r=modpow(2LL,x,N); if(r==1) ans=min(ans,x); } cout << ans << endl; } return 0; }