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 = input()
t = int(T)
i = 0
while i < t:
    try:
        N = input()
    except :
        break
    sk = N.split(" ")
    n = int(sk[0])
    k = int(sk[1])
    ls = list()
    if k>n or (n%2==1 and k%2==0):
        print("NO")
    elif n/k==1 and n%2==0 and k%2==1:
        print("NO")
    else:
        dv = n/k
        md = n%k
        if md%2 :
            j = 0
            while j < k:
                ls.append(int(n / k) - 1)
                j = j + 1
            if ls[0] == 0:
                print("NO")
                continue
            ls[0] = ls[0] + n - ls[0] * k
        else:
            j = 0
            while j < k:
                ls.append(int(n / k))
                j = j + 1
            ls[0] = ls[0] + md
        print("YES")
        print(*ls)
    i = i + 1