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 function(n, k):
    l_odd=[1]*(k-1)
    l_odd.append(n-sum(l_odd))
    condition1=True
    for i in l_odd:
        if i%2==0 or i<=0:
            condition1=False
            break
    if condition1:
        print('YES')
        print(*l_odd)
    condition2=True
    if not condition1:
        l_even=[2]*(k-1)
        l_even.append(n-sum(l_even))
        for j in l_even:
            if j%2!=0 or j<=0:
                condition2=False
                break
        if condition2:
            print('YES')
            print(*l_even)
    if condition1==False and condition2==False:
        print('NO')



if __name__=='__main__':
    t=int(input())
    for k1 in range(t):
        n, k=map(int, input().rstrip().split())
        function(n, k)