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, k, p = map(int, input().split())
# arr = list(map(int, input().split()))


def find(n, k):
    print("YES")
    ans = []
    count = n // k
    if n % 2 == 0 and k % 2 == 1:
        count = (count // 2) * 2
    if n % 2 == 1 and k % 2 == 1:
        count = count - 1 if count % 2 == 0 else count
    if count == 0:
        count
    n -= k * count
    for r in range(k):
        ans.append(count)
    if n != 0:
        ans[-1] += n
    answer = ""
    for a in ans:
        answer += str(a) + " "
    print(answer)


t = int(input())

for i in range(t):
    n, k = map(int, input().split())
    if k > n:
        print("NO")
    else:
        if n % 2 == 1:
            if k % 2 == 0:
                print("NO")
            else:
                find(n, k)
        else:
            if k % 2 == 1:
                if k * 2 > n:
                    print("NO")
                else:
                    find(n, k)
            else:
                find(n, k)