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())
while t>0:
    t-=1
    n, k = map(int,input().split())
    #now we want to make the sum n using k integers all odd or all even 
    odd = []
    kg = k
    kc = k
    nc = n
    if n < k:
        print("NO")
        continue
    while kc > 0 and nc>0:
        odd.append(1)
        kc-=1
        nc-=1
    if nc%2 == 0:
        odd.pop()
        odd.append(nc+1)
        if len(odd) == kg:  
            print("YES")
            for x in odd:
                print(x,end=" ")
            print()
        continue

    even = []
    while k>0 and n>0:
        even.append(2)
        k-=1
        n-=2
    if n%2==0:
        #now after appending all the elements and the remaining count we have is now even add to last bucket
        even.pop()
        even.append(n+2)
        if len(even) == kg:
            print("YES")
            for x in even :
                print(x,end=" ")
            print()
            continue
    print("NO")