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:
# accepted
t = int(input())
for i in range(t):
    n, k = map(int, input().split())
    if k > n or (n % 2 == 0 and k % 2 == 1 and k * 2 > n) or (n % 2 == 1 and k % 2 == 0):
        print('NO')
    else:
        N = []
        if k == 1:
            N.append(n)
        elif n == k:
            N = [1] * k
        elif n == k * 2:
            N = [2] * k
        elif n % 2 == 0 and k * 2 < n:
            N = [2] * (k - 1)
            N.append(n - 2 * (k - 1))
        else:
            N = [1] * (k - 1)
            N.append(n - k + 1)
        print('YES \n', *N)