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:
def print_list(arr):
  print('YES')
  for i in range(len(arr)):
    print(arr[i],end = ' ')
  print()


t = int(input())
for i in range(t):
  n,k = input().split()
  n = int(n)
  k = int(k)

  values0 = [n//k for i in range(k)]
  values1 = [(n//k)-1 for i in range(k)]

  if sum(values0) == n:
    print_list(values0)

  elif sum(values0) > 0:
    while sum(values0) < n:
      values0[0] += 2

    if sum(values0) == n:
      print_list(values0)
    
    elif (n//k)-1 > 0:
      while sum(values1) < n:
        values1[0] += 2

      if sum(values1) == n:
        print_list(values1)
      
      else:
        print('NO')
    
    else:
      print("NO")

  else:
    print("NO")