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 solve():
    n, k = map(int, input().split())
    if k > n:
        print("NO")
        return 
    lst = []
    n1 = n - (k-1)
    if n1 % 2 == 1 and n1>0:
        lst.extend([1]*(k-1))
        lst.append(n1)
        print("YES")
        print(*lst)
        return

    n2 = n - 2*(k-1)
    if n2 % 2 == 0 and n2 > 0:
        lst.extend([2]*(k-1))
        lst.append(n2)
        print("YES")
        print(*lst)
        return

    print("NO")

t = int(input())

while t:
    solve()
    
    t-=1

    






















'''t = int(input())
while t :
    k = 0
    x = int(input())
    lst = list(map(int, input().split()))
    my_lst = [0] * (x)
    for i, v in enumerate(lst):
        a = v % x
        my_lst[(i+a)%x] += 1
    #print(my_lst)
    for i in my_lst:
        if i > 1:
            k = 1
            break
    if k==1:
        print("NO")
    else:   
        print("YES")



    
    t-=1
'''