#include <iostream>
#include <vector>
#include <algorithm>

using namespace std;

vector<int> hamming_numbers(int n) {
    vector<int> res = {1};
    int i2 = 0, i3 = 0, i5 = 0;
    for (int i = 1; i < n; i++) {
        int next_2 = res[i2] * 2;
        int next_3 = res[i3] * 3;
        int next_5 = res[i5] * 5;
        int next = min(next_2, min(next_3, next_5));
        res.push_back(next);
        if (next == next_2) i2++;
        if (next == next_3) i3++;
        if (next == next_5) i5++;
    }
    return res;
}

int main() {
    int start, end;
    cout << "Enter the start and end number of the range to find hamming numbers here : ";
    cin >> start >> end;
    vector<int> hamming = hamming_numbers(end);
    cout << "Okay, the Hamming numbers in the given range interms of numbers are : " << endl;
    for (auto num : hamming) {
        if (num >= start) {
            cout << num << " ";
        }
    }
    cout << endl;
    return 0;
}