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(0,t):
   n, k = input().strip().split()
   n, k = int(n), int(k)
   if k%2==0 and n%2!=0:
       print("NO")
   elif k%2==0:
       if n>(k-1):
           print("YES")
           for i in range(k-1):
               print("1", end = " ")
           print(n-k+1)
       else:
           print('NO')
   else:
       if n%2==0 and n<2*k:
           print("NO")
       elif n%2==0:
           print("YES")
           for i in range(k-1):
               print("2", end =" ")
           print(n-2*(k-1))
       else:
           if n<k:
               print("NO")
           else:
               print("YES")
               for i in range(k-1):
                   print("1", end = " ")
               print(n-k+1)