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:
"""
Please FUCKING

      ***   *       *   *********        ***   *       *     ***
    **      *       *   *              **      *     **      ***
  **        *       *   *            **        *   **        ***
**          *********   *********  **          ***           ***
  **        *       *   *            **        *   **
    **      *       *   *              **      *     **      ***
      ***   *       *   *********        ***   *       *     ***

check 1: ok
check 2: mb
check 3: mb
"""
from sys import stdin


def inp():
    return stdin.buffer.readline().rstrip().decode("utf8")


def itg():
    return int(stdin.buffer.readline())


def mpint():
    return map(int, stdin.buffer.readline().split())

def solve():
    n, k = mpint()
    if (k % 2 == 0 and n & 1) or n < k:
        return "NO"
    if k == 1:
        return "YES\n%d" % n
    if n == k:
        print("YES")
        return ("1 "*k).rstrip()

    if n & 1:  # n, k is odd
        ans = [1]*(k-1)
        n -= k - 1
        if n <= 0 or n % 2 == 0:
            return "NO"
        ans.append(n)
        print("YES")
        return ' '.join(map(str, ans))

    # n is even
    if k & 1:
        ans = [2] * (k - 1)
        n -= 2 * (k - 1)  # still even
        if n <= 0:
            return "NO"
        ans.append(n)
        print("YES")
        return ' '.join(map(str, ans))

    # n, k is even
    ans = [1] * (k - 1)
    n -= k - 1
    if n <= 0 or n % 2 == 0:
        return "NO"

    ans.append(n)
    print("YES")
    return ' '.join(map(str, ans))

for case in range(itg()):
    print(solve())

# Please FUCKING check!