Problem: Bizon the Champion isn't just friendly, he also is a rigorous coder.

Let's define function f(a), where a is a sequence of integers. Function f(a) returns the following sequence: first all divisors of a1 go in the increasing order, then all divisors of a2 go in the increasing order, and so on till the last element of sequence a. For example, f([2, 9, 1]) = [1, 2, 1, 3, 9, 1].

Let's determine the sequence Xi, for integer i (i ≥ 0): X0 = [X] ([X] is a sequence consisting of a single number X), Xi = f(Xi - 1) (i > 0). For example, at X = 6 we get X0 = [6], X1 = [1, 2, 3, 6], X2 = [1, 1, 2, 1, 3, 1, 2, 3, 6].

Given the numbers X and k, find the sequence Xk. As the answer can be rather large, find only the first 105 elements of this sequence.

Input

A single line contains two space-separated integers — X (1 ≤ X ≤ 1012) and k (0 ≤ k ≤ 1018).

Output

Print the elements of the sequence Xk in a single line, separated by a space. If the number of elements exceeds 105, then print only the first 105 elements.

Examples

Input

6 1


Output

1 2 3 6 


Input

4 2


Output

1 1 2 1 2 4 


Input

10 3


Output

1 1 1 2 1 1 5 1 1 2 1 5 1 2 5 10 

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

import javafx.collections.transformation.SortedList;

public class Divisors {
    static long X; // 10^12
    static long k; // 10^18
    static long[] divisorIndex;
    static long[] divisors;

    public static void main(String[] args) throws IOException {
        initReader();
        while (true) {
            readInput();

            int result = solve();
            //testFactorization(X);
            //testAllDivisor(X);
            //testMap(X);

            break;
        }
    }

    public static int solve() {

        List<Long> divisors = new ArrayList<Long>();
        Map<Long, List<Long>> divisorMap = getDivisorsOfDivisor(X, divisors);

        /*
         * for (int i = 0; i < divisors.size(); i++) { long divisor =
         * divisors.get(i); System.out.print(divisor + ": "); List<Long>
         * children = divisorMap.get(divisor); for (int j = 0; j <
         * children.size(); j++) { System.out.print(children.get(j) + " "); }
         * System.out.println(""); }
         */

        Status[] stack = new Status[100001];

        int limit = 100000;
        int ik = (int) Math.min((long) limit, k);

        stack[0] = new Status(X, -1);
        int index = 0;
        int printed = 0;
        while (printed < limit && index >= 0) {
            Status current = stack[index];
            if (current.number == 1) {
                printed++;
                System.out.print(1 + (printed == limit ? "" : " "));
                index--;
                continue;
            }
            if (index == ik) {
                printed++;
                System.out
                        .print(current.number + (printed == limit ? "" : " "));
                index--;
                continue;
            }
            List<Long> children = divisorMap.get(current.number);
            if (current.index < children.size() - 1) {
                current.index++;
                long childDivisor = children.get(current.index);
                index++;
                stack[index] = new Status((long) childDivisor, -1);
            } else {
                index--;
            }
        }

        return 0;
    }

    // 10^12 < 2*3*5*7*11*13*17*19*23*29*31*37 => Maximum 2^11 ~ 2K divisors
    public static List<NumberFactor> fatorization(long x) {
        long sq = Math.round(Math.sqrt(x)) + 1; // 10 ^ 6
        List<NumberFactor> list = new ArrayList<NumberFactor>();
        int i = 2;
        NumberFactor current = null;
        while (i < sq && x > 1) {
            if (x % i == 0) {
                if (current == null) {
                    current = new NumberFactor(i, 0);
                    list.add(current);
                }
                current.base++;
                x = x / i;
            } else {
                current = null;
                i++;
            }
        }
        if (x > 1) {
            list.add(new NumberFactor(x, 1));
        }
        return list;
    }

    public static List<Long> getDivisors(long x) {
        List<Long> divisors = new ArrayList<Long>();
        divisors.add((long) 1);

        List<NumberFactor> factors = fatorization(x);

        for (int i = 0; i < factors.size(); i++) {
            NumberFactor factor = factors.get(i);
            int preCount = divisors.size();
            long item = 1;
            for (int base = 1; base <= factor.base; base++) {
                item *= factor.prime;
                for (int j = 0; j < preCount; j++) {
                    divisors.add(divisors.get(j) * item);
                }
            }
        }
        divisors.sort(comparator());
        return divisors;
    }

    public static Map<Long, List<Long>> getDivisorsOfDivisor(long x,
            List<Long> divisors) {

        Map<Long, List<Long>> divisorMap = new HashMap<Long, List<Long>>();
        List<Long> firstList = new ArrayList<Long>();
        firstList.add((long) 1);
        divisorMap.put((long) 1, firstList);

        divisors.add((long) 1);

        List<NumberFactor> factors = fatorization(x);

        for (int i = 0; i < factors.size(); i++) {
            NumberFactor factor = factors.get(i);
            int preCount = divisors.size();
            long item = 1;
            for (int base = 1; base <= factor.base; base++) {
                item *= factor.prime;
                for (int j = 0; j < preCount; j++) {
                    long oldDivisor = divisors.get(j);
                    long newDivisor = oldDivisor * item;
                    divisors.add(newDivisor);

                    List<Long> oldChildren = divisorMap.get(oldDivisor);
                    List<Long> newChildren = new ArrayList<Long>();
                    newChildren.addAll(oldChildren);
                    for (int u = 0; u < oldChildren.size(); u++) {
                        long newItem = 1;
                        while (newItem < item) {
                            newItem *= factor.prime;
                            newChildren.add(oldChildren.get(u) * newItem);
                        }
                    }
                    newChildren.sort(comparator());
                    divisorMap.put(newDivisor, newChildren);
                }
            }
        }

        return divisorMap;
    }

    public static Comparator<Long> comparator() {
        return new Comparator<Long>() {
            public int compare(Long arg0, Long arg1) {
                return Long.compare(arg0, arg1);
            }
        };
    }

    public static void testFactorization(long x) {
        List<NumberFactor> factors = fatorization(x);
        for (int i = 0; i < factors.size(); i++) {
            NumberFactor factor = factors.get(i);
            System.out.println(factor.prime + " " + factor.base);
        }
        System.out.println("");
    }

    public static void testAllDivisor(long x) {
        List<Long> divisors0 = getDivisors(X);
        System.out.print(divisors0.size() + ":    ");
        for (int i = 0; i < divisors0.size(); i++) {
            System.out.print(divisors0.get(i) + " ");
        }
        System.out.println("");
    }

    public static void testMap(long x) {
        List<Long> divisors = new ArrayList<Long>();
        Map<Long, List<Long>> divisorMap = getDivisorsOfDivisor(X, divisors);
        
        int total = 0;
        for (int i = 0; i < divisors.size(); i++) {
            long divisor = divisors.get(i);
            List<Long> children = divisorMap.get(divisor);
            total += children.size();
        }
        System.out.println(total);

        for (int i = 0; i < divisors.size(); i++) {
            long divisor = divisors.get(i);
            System.out.print(divisor + ": ");
            List<Long> children = divisorMap.get(divisor);
            for (int j = 0; j < children.size(); j++) {
                System.out.print(children.get(j) + " ");
            }
            System.out.println("");
        }
    }

    public static void readInput() throws IOException {
        X = nextLong();
        k = nextLong();
    }

    static BufferedReader reader;
    static StringTokenizer tokenizer;

    public static void initReader() {
        reader = new BufferedReader(new InputStreamReader(System.in));
        tokenizer = new StringTokenizer("");
    }

    static String next() throws IOException {
        while (!tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(reader.readLine());
        }
        return tokenizer.nextToken();
    }

    static String nextLine() throws IOException {
        return reader.readLine();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    static long nextLong() throws IOException {
        return Long.parseLong(next());
    }

    static Double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }
}

class NumberFactor {
    long prime;
    int base;

    public NumberFactor(long prime, int base) {
        this.prime = prime;
        this.base = base;
    }
}

class Status {
    long number;
    int index;

    public Status(long number, int index) {
        this.number = number;
        this.index = index;
    }
}

/*
 * class NumberDivisor { long number; List<Long> divisors = new
 * ArrayList<Long>(); }
 */

/*
 * List<NumberFactor> factors = fatorization(X); for (int i = 0; i <
 * factors.size(); i++) { NumberFactor factor = factors.get(i);
 * System.out.println(factor.prime + " " + factor.base); }
 * System.out.println("");
 */

/*
 * List<Long> divisors0 = getDivisors(X); System.out.print(divisors0.size());
 * for (int i = 0; i < divisors0.size(); i++) {
 * System.out.print(divisors0.get(i) + " "); } System.out.println("");
 */

/*
 * int total = 0; for (int i = 0; i < divisors.size(); i++) { long divisor =
 * divisors.get(i); List<Long> children = divisorMap.get(divisor); total +=
 * children.size(); } System.out.println(total);
 * 
 * for (int i = 0; i < divisors.size(); i++) { long divisor = divisors.get(i);
 * System.out.print(divisor + ": "); List<Long> children =
 * divisorMap.get(divisor); for (int j = 0; j < children.size(); j++) {
 * System.out.print(children.get(j) + " "); } System.out.println(""); }
 */