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 PYTHON3):

Solution:
t = int( input() )

for i in range( t ):
  l = input().split()
  n = int( l[0] )
  k = int( l[1] )

  v1 = k-1
  if v1 < n and (n-v1)%2==1:
    v1 = n
  else:
    v1 = 0 

  v2 = 2*(k-1)
  if v2 < n and (n-v2)%2==0:
    v2 = n
  else:
    v2 = 0

  if v1==n:
    print( "YES")
    if k > 1:
      for j in range( k-1 ):
        print( "1" , end = " " )
    print( n-(k-1) )
    continue
  if v2==n:
    print( "YES")
    if k > 1:
      for j in range( k-1 ):
        print( "2" , end = " " )
    print( n-2*(k-1) )
    continue
  
  print( "NO" )