#pragma GCC optimize ("Ofast")
#include<bits/stdc++.h>
using namespace std;
void*wmem;
char memarr[96000000];
template<class T> inline void walloc1d(T **arr, int x, void **mem = &wmem){
  static int skip[16] = {0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1};
  (*mem) = (void*)( ((char*)(*mem)) + skip[((unsigned long long)(*mem)) & 15] );
  (*arr)=(T*)(*mem);
  (*mem)=((*arr)+x);
}
struct Rand{
  unsigned x;
  unsigned y;
  unsigned z;
  unsigned w;
  Rand(void){
    x=123456789;
    y=362436069;
    z=521288629;
    w=(unsigned)time(NULL);
  }
  Rand(unsigned seed){
    x=123456789;
    y=362436069;
    z=521288629;
    w=seed;
  }
  inline unsigned get(void){
    unsigned t;
    t = (x^(x<<11));
    x=y;
    y=z;
    z=w;
    w = (w^(w>>19))^(t^(t>>8));
    return w;
  }
  inline double getUni(void){
    return get()/4294967296.0;
  }
  inline int get(int a){
    return (int)(a*getUni());
  }
  inline int get(int a, int b){
    return a+(int)((b-a+1)*getUni());
  }
  inline long long get(long long a){
    return(long long)(a*getUni());
  }
  inline long long get(long long a, long long b){
    return a+(long long)((b-a+1)*getUni());
  }
  inline double get(double a, double b){
    return a+(b-a)*getUni();
  }
  inline int getExp(int a){
    return(int)(exp(getUni()*log(a+1.0))-1.0);
  }
  inline int getExp(int a, int b){
    return a+(int)(exp(getUni()*log((b-a+1)+1.0))-1.0);
  }
}
;
inline int my_getchar_unlocked(){
  static char buf[1048576];
  static int s = 1048576;
  static int e = 1048576;
  if(s == e && e == 1048576){
    e = fread_unlocked(buf, 1, 1048576, stdin);
    s = 0;
  }
  if(s == e){
    return EOF;
  }
  return buf[s++];
}
inline void rd(int &x){
  int k;
  int m=0;
  x=0;
  for(;;){
    k = my_getchar_unlocked();
    if(k=='-'){
      m=1;
      break;
    }
    if('0'<=k&&k<='9'){
      x=k-'0';
      break;
    }
  }
  for(;;){
    k = my_getchar_unlocked();
    if(k<'0'||k>'9'){
      break;
    }
    x=x*10+k-'0';
  }
  if(m){
    x=-x;
  }
}
inline void rd(long long &x){
  int k;
  int m=0;
  x=0;
  for(;;){
    k = my_getchar_unlocked();
    if(k=='-'){
      m=1;
      break;
    }
    if('0'<=k&&k<='9'){
      x=k-'0';
      break;
    }
  }
  for(;;){
    k = my_getchar_unlocked();
    if(k<'0'||k>'9'){
      break;
    }
    x=x*10+k-'0';
  }
  if(m){
    x=-x;
  }
}
inline int rd_int(void){
  int x;
  rd(x);
  return x;
}
struct MY_WRITER{
  char buf[1048576];
  int s;
  int e;
  MY_WRITER(){
    s = 0;
    e = 1048576;
  }
  ~MY_WRITER(){
    if(s){
      fwrite_unlocked(buf, 1, s, stdout);
    }
  }
}
;
MY_WRITER MY_WRITER_VAR;
void my_putchar_unlocked(int a){
  if(MY_WRITER_VAR.s == MY_WRITER_VAR.e){
    fwrite_unlocked(MY_WRITER_VAR.buf, 1, MY_WRITER_VAR.s, stdout);
    MY_WRITER_VAR.s = 0;
  }
  MY_WRITER_VAR.buf[MY_WRITER_VAR.s++] = a;
}
inline void wt_L(char a){
  my_putchar_unlocked(a);
}
inline void wt_L(int x){
  int s=0;
  int m=0;
  char f[10];
  if(x<0){
    m=1;
    x=-x;
  }
  while(x){
    f[s++]=x%10;
    x/=10;
  }
  if(!s){
    f[s++]=0;
  }
  if(m){
    my_putchar_unlocked('-');
  }
  while(s--){
    my_putchar_unlocked(f[s]+'0');
  }
}
inline void wt_L(long long x){
  int s=0;
  int m=0;
  char f[20];
  if(x<0){
    m=1;
    x=-x;
  }
  while(x){
    f[s++]=x%10;
    x/=10;
  }
  if(!s){
    f[s++]=0;
  }
  if(m){
    my_putchar_unlocked('-');
  }
  while(s--){
    my_putchar_unlocked(f[s]+'0');
  }
}
template<class T> int Factor_L(T N, T fac[]){
  T i;
  int sz = 0;
  if(N%2==0){
    fac[sz] = 2;
    N /= 2;
    while(N%2==0){
      N /= 2;
    }
    sz++;
  }
  for(i=3;i*i<=N;i+=2){
    if(N%i==0){
      fac[sz] = i;
      N /= i;
      while(N%i==0){
        N /= i;
      }
      sz++;
    }
  }
  if(N > 1){
    fac[sz] = N;
    sz++;
  }
  return sz;
}
template<class T> int Factor_L(T N, T fac[], int fs[]){
  T i;
  int sz = 0;
  if(N%2==0){
    fac[sz] = 2;
    fs[sz] = 1;
    N /= 2;
    while(N%2==0){
      N /= 2;
      fs[sz]++;
    }
    sz++;
  }
  for(i=3;i*i<=N;i+=2){
    if(N%i==0){
      fac[sz] = i;
      fs[sz] = 1;
      N /= i;
      while(N%i==0){
        N /= i;
        fs[sz]++;
      }
      sz++;
    }
  }
  if(N > 1){
    fac[sz] = N;
    fs[sz] = 1;
    sz++;
  }
  return sz;
}
template<class T> int Divisor_L(T N, T res[], void *mem = wmem){
  int i;
  int j;
  int k;
  int s;
  int sz = 0;
  T*fc;
  int*fs;
  int fsz;
  walloc1d(&fc, 100, &mem);
  walloc1d(&fs, 100, &mem);
  fsz =Factor_L(N, fc, fs);
  res[sz++] = 1;
  for(i=(0);i<(fsz);i++){
    s = sz;
    k = s * fs[i];
    for(j=(0);j<(k);j++){
      res[sz++] = res[j] * fc[i];
    }
  }
  sort(res, res+sz);
  return sz;
}
unsigned long long powmod(unsigned long long a, unsigned long long b, unsigned long long m){
  unsigned long long r = 1;
  while(b){
    if(b&1){
      r = r * a % m;
    }
    b>>=1;
    a = a * a % m;
  }
  return r;
}
int fs;
long long f[200000];
int ds;
long long d[200000];
int main(){
  int Lj4PdHRW;
  wmem = memarr;
  Rand rnd;
  int KL2GvlyY = rd_int();
  for(Lj4PdHRW=(0);Lj4PdHRW<(KL2GvlyY);Lj4PdHRW++){
    int i;
    long long N;
    rd(N);
    long long res;
    long long phi;
    if(N==1){
      wt_L(1);
      wt_L('\n');
      continue;
    }
    N = 2 * N - 1;
    fs =Factor_L(N, f);
    phi = N;
    for(i=(0);i<(fs);i++){
      phi = phi * (f[i]-1) / f[i];
    }
    ds =Divisor_L(phi, d);
    for(i=(0);i<(ds);i++){
      if(powmod(2, d[i], N) == 1){
        res = d[i];
        break;
      }
    }
    wt_L(res);
    wt_L('\n');
  }
  return 0;
}
// cLay varsion 20201003-1

// --- original code ---
// int fs; ll f[2d5];
// int ds; ll d[2d5];
// {
//   Rand rnd;
//   REP(rd_int()){
//     ll @N, res, phi;
//     if(N==1) wt(1), continue;
//     N = 2 * N - 1;
//     fs = Factor(N, f);
//     phi = N;
//     rep(i,fs) phi = phi * (f[i]-1) / f[i];
//     ds = Divisor(phi, d);
//     rep(i,ds) if(powmod(2, d[i], N) == 1) res = d[i], break;
//     wt(res);
//   }
// }