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 _ in range(t):
    n, k = map(int, input().split())
    ans = []
    good = False
    p = False
    
    # possible with even
    if n % 2 == 0 and k <= n/2:
        good = True
        x = 0
        while x < k:
            if x + 1 == k:
                if n - sum(ans) > 0 and (n-sum(ans)) % 2 == 0:
                    ans.append(n - sum(ans))
                else:
                    good = False
            else:
                ans.append(2)
            x += 1

        if good:
            p = True
            print('YES')
            print(*ans)

    # possible with odd
    if k <= n and not p:
        good = True
        x = 0
        while x < k:
            # last
            if x + 1 == k:
                # correct
                if n - sum(ans) > 0 and (n-sum(ans)) % 2 == 1:
                    ans.append(abs(n - sum(ans)))
                else:
                    good = False
                    
            else:
                ans.append(1)
            x += 1

        if good:
            p = True
            print("YES")
            print(*ans)

    # nothing got printed
    if not p:
        print('NO')