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:

def even(n, k, a):
    if n <= k:
        return False

    if n % k == 0 and (n // k) % 2 == 0:
        for i in range(k):
            a.append(n // k)
        return True

    a.append(2)
    return even(n-2, k-1, a)


def odd(n, k, a):
    if n < k:
        return False

    if n % k == 0 and (n // k) % 2 == 1:
        for i in range(k):
            a.append(n // k)
        return True

    a.append(1)
    return odd(n-1, k-1, a)

def summands(n, k):

    if n < k:
        return "NO", []

    if n % k == 0:
        return "YES", [n // k for i in range(k)]

    a, b = [], []
    if n % 2 == 0 and k % 2 == 1:
        if even(n, k, a):
            return "YES", a
        else:
            return "NO", []

    if n % 2 == 0 and k % 2 == 0:
        if even(n, k, a):
            return "YES", a
        elif odd(n, k, b):
            return "YES", b
        else:
            return "NO", []

    if n % 2 == 1 and k % 2 == 0:
        return "NO", []

    if n % 2 == 1 and k % 2 == 1:
        if odd(n, k, a):
            return "YES", a
        else:
            return "NO", []


t = int(input())
for i in range(t):
    a = input().split()
    n = int(a[0])
    k = int(a[1])
    ans, li = summands(n, k)
    print(ans)
    if ans:
        print(*li)