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:
n = int(input())

ans = []
for i in range(n):

    a, b = map(int, input().split())
    b -= 1
    if a - 2 * b > 0 and (a - 2 * b) % 2 != 1:
        ans.append([2, b, a - 2 * b])

    elif a - 1 * b > 0 and (a - 1 * b) % 2 != 0:
        ans.append([1, b, a - 1 * b])
    else:
        ans.append([-1])
for i in range(n):
    if len(ans[i]) == 1:
        print("NO")
    else:
        print("YES")
        for j in range(ans[i][1]):
            print(ans[i][0], end=' ')
        print(ans[i][2])