You are given positive integer number n. You should create such strictly increasing sequence of k positive numbers a1, a2, ..., ak, that their sum is equal to n and greatest common divisor is maximal.

Greatest common divisor of sequence is maximum of such numbers that every element of sequence is divisible by them.

If there is no possible sequence then output -1.

Input

The first line consists of two numbers n and k (1 ≤ n, k ≤ 1010).

Output

If the answer exists then output k numbers — resulting sequence. Otherwise output -1. If there are multiple answers, print any of them.

Examples

Input

6 3


Output

1 2 3


Input

8 2


Output

2 6


Input

5 3


Output

-1
import java.util.*;
import java.io.*;
import java.math.*;
public class test{
	static long n,k;
	public static void main(String[] args)throws Exception{
		n = nextLong();
		k = nextLong();
		if(k > 200000 || k*(k+1)/2 > n){
			System.out.println(-1);
			return;
		}

		long rn = (long)Math.sqrt(n);
		long ans = -1;
		for(long i=1;i<=rn;i++) {
			if(n%i==0) {
				ans = Math.max(ans,check(i));
				ans = Math.max(ans,check(n/i));
			}
		}
		if(ans==-1)
			System.out.println(ans);
		else {
			for(long i=1;i<k;i++) {
				System.out.print((i*ans)+" ");
			}
			long sum = ans*k*(k-1)/2;
			System.out.println(n-sum);
		}
 	}

 	static long check(long d) {
 		long sum = d*k*(k-1)/2;
 		if(n-sum > (k-1)*d && (n-sum)%d==0)
 			return d;
 		return -1;
 	}

	static boolean isPrime(int n){
		for(int i=2;i<n;i++){
			if(n%i==0){
				return false;
			}
		}
		return true;
	}
	static int nextInt()throws IOException{
		InputStream in=System.in;
		int ans=0;
		boolean flag=true;
		byte b=0;
		boolean neg=false;
		while ((b>47 && b<58) || flag){
			if(b==45)
				neg=true;
			if(b>=48 && b<58){
				ans=ans*10+(b-48);
				flag=false;
			}
			b=(byte)in.read();
		}
		if(neg)
			return -ans;
		return ans;
	}
	static int gcd(int a,int b){
		if(b==0)
			return a;
		return gcd(b,a%b);
	}

	static long nextLong()throws IOException{
		InputStream in=System.in;
		long ans=0;
		boolean flag=true;
		byte b=0;
		while ((b>47 && b<58) || flag){
			if(b>=48 && b<58){
				ans=ans*10+(b-48);
				flag=false;
			}
			b=(byte)in.read();
		}
		return ans;
	}
	static String next()throws Exception{
		StringBuilder sb=new StringBuilder(1<<16);
		InputStream in=System.in;
		byte b=0;
		do{
			if(!isWhiteSpace(b))
				sb.append((char)b);
			b=(byte)in.read();
		}while(!isWhiteSpace(b) || sb.length()==0);
		return sb.toString();
	}
	static boolean isWhiteSpace(byte b){
		char ch=(char)b;
		return ch=='\0' || ch==' ' || ch=='\n';
	}
}