Problem: Daniel is organizing a football tournament. He has come up with the following tournament format: 

  1. In the first several (possibly zero) stages, while the number of teams is even, they split in pairs and play one game for each pair. At each stage the loser of each pair is eliminated (there are no draws). Such stages are held while the number of teams is even. 
  2. Eventually there will be an odd number of teams remaining. If there is one team remaining, it will be declared the winner, and the tournament ends. Otherwise each of the remaining teams will play with each other remaining team once in round robin tournament (if there are x teams, there will be <image> games), and the tournament ends. 



For example, if there were 20 teams initially, they would begin by playing 10 games. So, 10 teams would be eliminated, and the remaining 10 would play 5 games. Then the remaining 5 teams would play 10 games in a round robin tournament. In total there would be 10+5+10=25 games.

Daniel has already booked the stadium for n games. Help him to determine how many teams he should invite so that the tournament needs exactly n games. You should print all possible numbers of teams that will yield exactly n games in ascending order, or -1 if there are no such numbers.

Input

The first line contains a single integer n (1 ≤ n ≤ 1018), the number of games that should be played.

Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.

Output

Print all possible numbers of invited teams in ascending order, one per line. If exactly n games cannot be played, output one number: -1.

Examples

Input

3


Output

3
4


Input

25


Output

20


Input

2


Output

-1

Solution (in JAVA):

Solution:
import static java.math.BigInteger.ONE;
import static java.math.BigInteger.ZERO;

import java.math.BigInteger;
import java.util.Scanner;
import java.util.SortedSet;
import java.util.TreeSet;

public class Cf325b {

    private static final BigInteger MINUS_ONE = BigInteger.valueOf(-1);
    private static final BigInteger TWO = BigInteger.valueOf(2);
    private static final BigInteger THREE = BigInteger.valueOf(3);
    private static final BigInteger FOUR = BigInteger.valueOf(4);
    private static SortedSet<BigInteger> result = new TreeSet<BigInteger>();

    public static BigInteger sqrt(BigInteger a) {
        final int bitLength = a.bitLength();
        BigInteger result = ONE.shiftLeft(bitLength / 2);
        while (!isSqrt(a, result)) {
            result = result.add(a.divide(result)).divide(TWO);
        }
        return result;
    }

    private static boolean isSqrt(BigInteger n, BigInteger root)
    {
        final BigInteger lowerBound = root.pow(2);
        final BigInteger upperBound = root.add(BigInteger.ONE).pow(2);
        return lowerBound.compareTo(n) <= 0
                && n.compareTo(upperBound) < 0;
    }

    public static boolean isOdd(BigInteger a) {
        return a.divideAndRemainder(TWO)[1].compareTo(ZERO) != 0;
    }

    public static void solve(BigInteger a, BigInteger b, BigInteger c, Integer k) {
        BigInteger D = b.multiply(b).subtract(FOUR.multiply(a).multiply(c));
        BigInteger sd = sqrt(D);
        if (sd.multiply(sd).compareTo(D) != 0) {
            return;
        }
        BigInteger mb = MINUS_ONE.multiply(b);
        BigInteger ta = TWO.multiply(a);
        BigInteger[] x1 = (mb.add(sd)).divideAndRemainder(ta);
        if (x1[1].compareTo(ZERO) == 0 && x1[0].compareTo(ZERO) > 0 && isOdd(x1[0])) {
            if (k == null) {
                result.add(x1[0]);
            } else {
                BigInteger x = x1[0];
                BigInteger r = x.multiply(TWO.pow(k));
                result.add(r);
            }
        }

        BigInteger[] x2 = (mb.subtract(sd)).divideAndRemainder(ta);
        if (x2[1].compareTo(ZERO) == 0 && x2[0].compareTo(ZERO) > 0 && isOdd(x2[0])) {
            if (k == null) {
                result.add(x2[0]);
            } else {
                BigInteger x = x2[0];
                BigInteger r = x.multiply(TWO.pow(k));
                result.add(r);
            }
        }
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        BigInteger n = new BigInteger(sc.next());
        BigInteger minusTwoN = MINUS_ONE.multiply(TWO).multiply(n);
        solve(ONE, MINUS_ONE, minusTwoN, null);
        for (int k = 1; k <= 66; k++) {
            solve(ONE, TWO.pow(k + 1).subtract(THREE), minusTwoN, k);
        }
        if (!result.isEmpty()) {
            for (BigInteger value : result) {
                System.out.println(value.toString());
            }
        } else {
            System.out.println(-1);
        }
        System.exit(0);
    }
}