may be hard on time, but as clear as possible

#include <iostream>
#include <set>
#include <cmath>
#include <string>

using namespace std;

int main() {
    long long k = 0;
    set<long long> v;
    v.insert(0);
    for (long long i = 0; i < 2147483648;){
        i = *prev(v.end()) + (++k);
        v.insert(i);
    }

    long long number;
    cin >> number;
    long long n;
    string word;
    for (size_t i = 0; i < number; i++) {
        cin >> n;
        if (v.find(n-1) != v.end())
            word += '1';
        else
            word += '0';
        word += ' ';
    }

    cout << word << endl;

    return 0;
}