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.*;
import java.util.*;

public class R256qEDivisors {

	static InputReader in;
	static PrintWriter w;
	static int cnt = 0;
	static ArrayList<Long> divisors[];
	static HashMap<Long,Integer> hash;
	static long k;
	
	@SuppressWarnings("unchecked")
	public static void main(String args[]) {
		in = new InputReader(System.in);
		w = new PrintWriter(System.out);
		
		long x = in.nextLong();
		k = in.nextLong();
		
		divisors = new ArrayList[7001];
		hash = new HashMap<Long,Integer>();
		int cnt1 = 0;
		divisors[0] = new ArrayList<Long>();
		hash.put(x, cnt1);
		
		for(long i=1;i*i<=x;i++){
			if(x % i == 0){
				divisors[0].add(i);
				if(i*i != x)
					divisors[0].add(x/i);
			}
		}
		
		Collections.sort(divisors[0]);
		
		for(long y : divisors[0]){
			cnt1++;
			hash.put(y, cnt1);
			divisors[cnt1] = new ArrayList<Long>();

			for(int j=0;j<cnt1;j++)
				if(y % divisors[0].get(j) == 0)
					divisors[cnt1].add(divisors[0].get(j));
		}
		
		if(k >= 100000){
			if(x == 1)
				w.print(1);
			else
				for(int i=1;i<=100000;i++)
					w.print("1 ");
		}
		else		
			dfs(x,0);
		w.println();
		
		w.close();
	}
	
	static void dfs(long x,int level){
		if(cnt >= 100000 || level > k)
			return;
		if(x == 1 || level == k){
			w.print(x + " ");
			cnt++;
		}
		else{
			int map = hash.get(x);
			for(long y : divisors[map]){
				dfs(y,level+1);
				if(cnt >= 100000)
					return;
			}
		}
	}
	
	static class InputReader {

		private InputStream stream;
		private byte[] buf = new byte[8192];
		private int curChar;
		private int snumChars;
		private SpaceCharFilter filter;

		public InputReader(InputStream stream) {
			this.stream = stream;
		}

		public int snext() {
			if (snumChars == -1)
				throw new InputMismatchException();
			if (curChar >= snumChars) {
				curChar = 0;
				try {
					snumChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (snumChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		public int nextInt() {
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = snext();
			}

			int res = 0;

			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));

			return res * sgn;
		}
		
		public long nextLong() {
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = snext();
			}

			long res = 0;

			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));

			return res * sgn;
		}
		
		public String readString() {
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = snext();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		public boolean isSpaceChar(int c) {
			if (filter != null)
				return filter.isSpaceChar(c);
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		public interface SpaceCharFilter {
			public boolean isSpaceChar(int ch);
		}
	}
}