Problem: You are given two positive integers n (1 ≤ n ≤ 10^9) and k (1 ≤ k ≤ 100). Represent the number n as the sum of k positive integers of the same parity (have the same remainder when divided by 2).

In other words, find a_1, a_2, …, a_k such that all a_i>0, n = a_1 + a_2 + … + a_k and either all a_i are even or all a_i are odd at the same time.

If such a representation does not exist, then report it.

Input

The first line contains an integer t (1 ≤ t ≤ 1000) — the number of test cases in the input. Next, t test cases are given, one per line.

Each test case is two positive integers n (1 ≤ n ≤ 10^9) and k (1 ≤ k ≤ 100).

Output

For each test case print:

  * YES and the required values a_i, if the answer exists (if there are several answers, print any of them); 
  * NO if the answer does not exist. 



The letters in the words YES and NO can be printed in any case.

Example

Input


8
10 3
100 4
8 7
97 2
8 8
3 10
5 3
1000000000 9


Output


YES
4 2 4
YES
55 5 5 35
NO
NO
YES
1 1 1 1 1 1 1 1
NO
YES
3 1 1
YES
111111110 111111110 111111110 111111110 111111110 111111110 111111110 111111110 111111120

Solution (in PYTHON):

Solution:
'''from sys import stdin, stdout
from random import randint
t=int(raw_input().strip())
for i in range(t):
    
    
    
    for j in range(n-1):
        print randint(1,m+1),
        l1=[int(x) for x in stdin.readline().strip().split()]
    
    l2=[int(x) for x in stdin.readline().strip().split()]
    print randint(1,m)
    '''

from random import randint
from sys import stdin
t=int(raw_input().strip())
for i in range(t):
    l=[int(x) for x in stdin.readline().strip().split()]
    n=l[0]
    k=l[1]
    if(n%2==1 and k%2==0):
        print "NO"
    elif(n%2==1 or (n%2==0 and k%2==0)):
        if(k>n):
            print "NO"
        else:
            print "YES"
            for i in range(0,k-1):
                print 1,
            print n-k+1
    else:
        if k*2>n:
            print "NO"

        else:
            print "YES"
            for i in range(0,k-1):
                print 2,
            print n-2*(k-1)