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:
#CODING IS LIFE
for __ in range(int(input())):
  n,k=map(int,input().split())
  l=[]
  s=0
  f=0
  c=0
  for i in range(k):
    if s>=n:
      break
    if i!=k-1:
      l.append(2)
      s+=2
    if i==k-1:
      p=n-s
      if p%2==0:
        f=1
        l.append(n-s)
        c+=1
  if f==0:
    l.clear()
    s=0
    for i in range(k):
      if s>=n:
        break
      if i!=k-1:
        l.append(1)
        s+=1
      if i==k-1:
        p=n-s
        if p%2!=0:
          l.append(n-s)
          c+=1
  if c==0:
    print('NO')
  else:
    print('YES') 
    for i in range(k):
      print(l[i],end=' ') 
    print()