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 solve(n,k):
    if n < k:
        return "NO"
    # odd
    ones = k - 1
    twos = (k - 1) * 2
    res = []
    if (n - k + 1) % 2 == 1 and (n - k + 1) > 0 :
        for i in range(k - 1):
            res.append(1)
        res.append(n - k + 1)
        return res
    elif (n - twos) > 0 and (n - twos) % 2 == 0:
        for i in range(k - 1):
            res.append(2)
        res.append(n - twos)
        return res
    return "NO"
    
def main():
    t = int(input())
    for i in range(t):
        d = input()
        d = [int(i) for i in d.split(" ")]
        n = d[0]
        a = d[1]
        ans = solve(n,a) 
        if ans == "NO":
            print(ans)                  
        else:
            print("YES")
            for i in ans:
                print(i,end = " ")
            print()
main()