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:
t = int(input())
q = []
for i in range(t):
    l = list(input().split())
    n = int(l[0])
    k = int(l[1])
    if k > n:
        q.append("NO")
    elif (n % 2 != 0) and (k % 2 == 0):
        q.append("NO")
    elif k == n:
        q.append("YES")
        q.append([1] * n)
    elif n % 2 != 0:
        q.append("YES")
        a = [1] * (k - 1)
        a.append(n - (k - 1))
        q.append(a)
    elif k <= (n // 2):
        q.append("YES")
        a = [2] * (k - 1)
        a.append(n - (2 * (k - 1)))
        q.append(a)
    elif k > (n // 2) and (k % 2 != 0):
        q.append("NO")
    else:
        q.append("YES")
        a = [1] * (k - 1)
        a.append(n - (k - 1))
        q.append(a)
i = 0
while i <= len(q) - 1:
    print(q[i])
    if q[i] == "YES":
        i += 1
        for j in q[i]:
            print(j, end=" ")
        print()
        i += 1
    else:
        i += 1