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:

T = input()
for t in range(T) :
  N, K = map(int,raw_input().split())
  
  '''
  ans = []
  if N < K : print 'NO'
  elif N%2 == 0 and K*2 <= N :
    for k in range(K-1) : ans.append(2)
    ans.append(N-2*(K-1))
    print "YES"
    print ' '.join(str(x) for x in ans)
  elif N%2 == 0 and N == K :
    ans = [1] * K
    print "YES"
    print ' '.join(str(x) for x in ans)
  elif N%2 == 1 and K%2 == 1 :
    for k in range(K-1) : ans.append(1)
    ans.append(N-K+1)
    print "YES"
    print ' '.join(str(x) for x in ans)
  else : print "NO"
  '''

  if K > N : print "NO"
  else :
    ans = []
    o, e = (N-(K-1)), (N-2*(K-1))
    if o % 2 == 1 and o > 0 : 
      for k in range(K-1) : ans.append(1)
      ans.append(N-K+1)
      print "YES"
      print ' '.join(str(x) for x in ans)
    elif e % 2 == 0 and e > 0 : 
      for k in range(K-1) : ans.append(2)
      ans.append(N-2*(K-1))
      print "YES"
      print ' '.join(str(x) for x in ans)
    else : print "NO"