INVDIV - Smallest Inverse Sum of Divisors.cpp

///   BISMILLAHIR RAHMANIR RAHEEM
///   ALLAH IS WATCHING ME


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///   ALLAH save us from COVID-19.Amin.

///   Every soul shall taste death.

///   Tag ::

/*
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                                    #BoycottFrenceProducts
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*/

#include<bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/detail/standard_policies.hpp>



///  order_of_key return number of elements less than x.
///  find_by_order return index.
using namespace std;
using namespace __gnu_pbds;


#define MOHAMMAD        ios::sync_with_stdio(0);cin.tie(0);
#define all(x)          (x).begin(), (x).end()
#define AE              cout << fixed << setprecision(10);
#define ld              double


/// faster.
#pragma GCC optimize("Ofast")
#pragma GCC target("avx,avx2,fma")

int dx8[] = {0, 0, 1, 1, 1, -1, -1, -1}; // 8-direction.......
int dy8[] = {1,-1, 1, -1, 0, 0, -1, 1};
int dx4[]= {1,-1,0,0}; // 4-direction...........
int dy4[]= {0,0,1,-1};


using ll = long long;
const ll MOD = 998244353 ;

bool check ( ll a , ll b ){
    return (a - (b*(a/b))) == 0;
}


typedef tree< int, null_type, less<int>, rb_tree_tag,tree_order_statistics_node_update> ordered_set;
typedef tree<pair<int, int>,null_type,less<pair<int, int>>,rb_tree_tag,tree_order_statistics_node_update> ordered_multiset;

//debug
template<typename F,typename S>ostream&operator<<(ostream&os,const pair<F,S>&p){return os<<"("<<p.first<<", "<<p.second<<")";}
template<typename T>ostream&operator<<(ostream&os,const vector<T>&v){os<<"{";for(auto it=v.begin();it!=v.end();++it){if(it!=v.begin())os<<", ";os<<*it;}return os<<"}";}
template<typename T>ostream&operator<<(ostream&os,const set<T>&v){os<<"[";for(auto it=v.begin();it!=v.end();++it){if(it!=v.begin())os<<",";os<<*it;}return os<<"]";}
template<typename T>ostream&operator<<(ostream&os,const multiset<T>&v) {os<<"[";for(auto it=v.begin();it!=v.end();++it){if(it!=v.begin())os<<", ";os<<*it;}return os<<"]";}
template<typename F,typename S>ostream&operator<<(ostream&os,const map<F,S>&v){os<<"[";for(auto it=v.begin();it!=v.end();++it){if(it!=v.begin())os<<", ";os<<it->first<<" = "<<it->second;}return os<<"]";}
#define dbg(args...) do {cerr << #args << " : "; faltu(args); } while(0)
void faltu(){cerr << endl;}
template<typename T>void faltu(T a[],int n){for(int i=0;i<n;++i)cerr<<a[i]<<' ';cerr<<endl;}
template<typename T,typename...hello>void faltu(T arg,const hello&...rest){cerr<<arg<<' ';faltu(rest...);}
//#else
//#define dbg(args...)

/// Modular arithmetic
inline void normal(ll &a) { a %= MOD; (a < 0) && (a += MOD); }
inline ll modMul(ll a, ll b) { a %= MOD, b %= MOD; normal(a), normal(b); return (a*b)%MOD; }
inline ll modAdd(ll a, ll b) { a %= MOD, b %= MOD; normal(a), normal(b); return (a+b)%MOD; }
inline ll modSub(ll a, ll b) { a %= MOD, b %= MOD; normal(a), normal(b); a -= b; normal(a); return a; }
inline ll modPow(ll b, ll p) { ll r = 1; while(p) { if(p&1) r = modMul(r, b); b = modMul(b, b); p >>= 1; } return r; }
inline ll modInverse(ll a) { return modPow(a, MOD-2); }  /// When MOD is prime.
inline ll modDiv(ll a, ll b) { return modMul(a, modInverse(b)); }

//***********************************************  The END **********************************************************************************************************************************
const int N = 1e8 + 1;
const ll INF = 1e18;
const ll limit = (1LL<<64) - 1;
const ld EPS   = 1e-6;
const ll K = 1e5 + 1;


/// Global...

int sigma[N] , ans[N];

void sieve ( ){   /// sigma using nloglogn.
 fill ( sigma , sigma+N , 1 );

 for ( int i = 2 ; i < N ; i++ ){
      if ( sigma[i]!=1 ) continue;
      for ( int j = i ; j < N ; j+=i ){
           int cur = j;
           int p = 1;
           int multi = 1;
           while ( cur % i == 0 ){ /// 1 + p^1 + p^2 + p^3 .... p^n.
               cur/=i;
               p*=i;
               multi+=p;
           }
           sigma[j]*=multi;
      }
 }
}

void solve ( ){

  int n;
  cin >> n;
  if ( ans[n] == 0 ) cout << "-1\n";
  else cout << ans[n] << "\n";

  return;
}


int main()
{
    MOHAMMAD

    /*
    #ifdef OJ
        freopen("input.txt", "r", stdin);
        freopen("output.txt", "w", stdout);
    #endif
    */
    sieve( );

    for ( int i = 1 ; i < N ; ++i ){
         /// dbg ( i , sigma[i] );
        if (  sigma[i] < N and ans[sigma[i]] == 0  ){
            ans[sigma[i]] = i;
        }
    }

    int t = 1 , tc = 0;
    cin >> t;


    while ( t-- ){
       solve(  );
    }
}



/*
Explanation:





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  Alhamdulillah
*/