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
# python2
import sys, threading, os.path
import collections, heapq, math 

sys.setrecursionlimit(10**6) # max depth of recursion
threading.stack_size(2**27)

divs = set()
def generate_divisors(n):
    i = 1
    while True:
        if i*i>n:
            break
        if n%i==0:
            divs.add(i)
            divs.add(n/i)
        i+=1

def main():
    if os.path.exists('input.txt'):
        input = open('input.txt', 'r')
    else:
        input = sys.stdin
    #--------------------------------INPUT---------------------------------
    n,k = list(map(int, input.readline().split()))
    generate_divisors(n)
    lis1 = list(sorted(divs,reverse = True))
    res = []
    for i,x in enumerate(lis1):
        tempN,tempK,tempCount,nice = n,k,1,True
        tempRes = []
        while True:
            
            if (tempN<=0 and tempK>0) or (x*tempCount>tempN):
                nice = False
                break
            if tempK==1 and tempN%x==0:
                tempRes.append(tempN)
                nice = True
                break
            
            tempN-=x*tempCount
            tempRes.append(x*tempCount)
            tempK-=1
            tempCount+=1
        if nice:
            res = tempRes
            break
        #print x,nice



    #print lis1
    if len(res)==k:
        output = ' '.join(map(str, res))
    else:
        output = -1
    #-------------------------------OUTPUT----------------------------------
    if os.path.exists('output.txt'):
        open('output.txt', 'w').writelines(str(output))
    else:
        sys.stdout.write(str(output))


if __name__ == "__main__":
    main()
