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 java.lang.StringBuffer;

import sun.font.CreatedFontTracker;

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();
        logTime("");
        while (true) {

            readInput();
            // logTime("readInput");

            solve();
            // logTime("solution");

            break;
        }
    }

    public static int solve() {

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

        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;
        StringBuffer stringBuffer = new StringBuffer();
        while (printed < limit && index >= 0) {
            Status current = stack[index];
            if (current.number == 1) {
                printed++;
                // System.out.print(1 + (printed == limit ? "" : " "));
                stringBuffer.append(1 + (printed == limit ? "" : " "));
                index--;
                continue;
            }
            if (index == ik) {
                printed++;
                // System.out
                // .print(current.number + (printed == limit ? "" : " "));
                stringBuffer.append(current.number
                        + (printed == limit ? "" : " "));
                index--;
                continue;
            }
            List<Long> children = divisorMap.get(current.number);
            /*
            if (children.size() == 2 && current.index == -1) {
                int need = Math.min(ik - index, limit - printed);
                String newString = initString(1'', need);
                printed += need;
                stringBuffer.append(newString);
                if (printed < limit) {
                    stringBuffer.append(current.number);
                    printed++;
                }
                index--;
                continue;
            }*/
            if (current.index < children.size() - 1) {
                current.index++;
                long childDivisor = children.get(current.index);
                index++;
                stack[index] = new Status((long) childDivisor, -1);
            } else {
                index--;
            }
        }
        System.out.print(stringBuffer.toString());
        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();
    }

    /*****************************************************************
     ******************** BASIC READER *******************************
     *****************************************************************/

    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());
    }

    /*****************************************************************
     ******************** TIME UTILITIES *******************************
     *****************************************************************/

    static long startTime = 0;
    static long preLogTime = 0;

    static void logTime(String lable) {
        long current = System.currentTimeMillis();
        if (startTime != 0) {
            println(lable, " - From start:", (current - startTime),
                    "- From previous:", (current - preLogTime));
        } else {
            startTime = current;
        }
        preLogTime = current;
    }

    /*****************************************************************
     ******************** READ UTILITIES *******************************
     *****************************************************************/

    public static int[] readLine(int n) throws IOException {
        int[] result = new int[n];
        for (int i = 0; i < n; i++) {
            result[i] = nextInt();
        }
        return result;
    }

    public static long[] readLineLong(int n) throws IOException {
        long[] result = new long[n];
        for (int i = 0; i < n; i++) {
            result[i] = nextLong();
        }
        return result;
    }

    public static int[][] readMatrix(int row, int column) throws IOException {
        int[][] result = new int[row][column];
        for (int i = 0; i < row; i++) {
            for (int j = 0; j < column; j++) {
                result[i][j] = nextInt();
            }
        }
        return result;
    }

    public static long[][] readMatrixLong(int row, int column)
            throws IOException {
        long[][] result = new long[row][column];
        for (int i = 0; i < row; i++) {
            for (int j = 0; j < column; j++) {
                result[i][j] = nextLong();
            }
        }
        return result;
    }

    /*****************************************************************
     ******************** PRINT UTILITIES *******************************
     *****************************************************************/

    public static void print(Object... obj) {
        System.out.print(join(obj, " "));
    }

    public static void println(Object... obj) {
        System.out.println(join(obj, " "));
    }

    public static String join(Object[] objs) {
        return join(objs, " ");
    }

    public static String join(int[] objs) {
        return join(objs, " ");
    }

    public static String join(long[] objs) {
        return join(objs, " ");
    }

    public static String join(Object[] objs, String glue) {
        if (objs.length == 0) {
            return "";
        }
        StringBuilder sb = new StringBuilder();
        int i;
        for (i = 0; i < objs.length - 1; i++) {
            sb.append(objs[i] + glue);
        }
        return sb.toString() + objs[i];
    }

    public static String join(int[] objs, String glue) {
        if (objs.length == 0) {
            return "";
        }
        StringBuilder sb = new StringBuilder();
        int i;
        for (i = 0; i < objs.length - 1; i++) {
            sb.append(objs[i] + glue);
        }
        return sb.toString() + objs[i];
    }

    public static String join(long[] objs, String glue) {
        if (objs.length == 0) {
            return "";
        }
        StringBuilder sb = new StringBuilder();
        int i;
        for (i = 0; i < objs.length - 1; i++) {
            sb.append(objs[i] + glue);
        }
        return sb.toString() + objs[i];
    }

    public static void printMatrix(int[][] matrix) {
        for (int i = 0; i < matrix.length; i++) {
            println(join(matrix[i]));
        }
    }

    public static void printMatrix(long[][] matrix) {
        for (int i = 0; i < matrix.length; i++) {
            println(join(matrix[i]));
        }
    }

    /*****************************************************************
     *************** ARRAY AND STRING UTILITIES **********************
     *****************************************************************/

    public static int[] initArray(int value, int length) {
        int[] result = new int[length];
        Arrays.fill(result, value);
        return result;
    }

    public static long[] initArray(long value, int length) {
        long[] result = new long[length];
        Arrays.fill(result, value);
        return result;
    }

    public static String initString(char c, int length) {
        char[] chars = new char[length];
        Arrays.fill(chars, c);
        return new String(chars);
    }
}

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;
    }
}