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 to_list(s):
    return list(map(lambda x: int(x), s.split(' ')))

def assemble(n,k):
    answer = []
    if k > n:
        return "NO"
    else:
        if (n % 2 == 0) & (k % 2 == 1):
            if  k > n / 2:
                return("NO")
            else:
                for i in range(k-1):
                    answer.append(2)
                answer.append(n-(k-1)*2)
                return(" ".join(list(map(lambda x: str(x),answer))))
        if (n % 2 == 0) & (k % 2 == 0):
            if n / 2 > k:
                for i in range(k-1):
                    answer.append(2)
                answer.append(n-(k-1)*2)
                return(" ".join(list(map(lambda x: str(x),answer))))
            else:
                if n / k == 1:
                    return " ".join([str(1) for i in range(n)])
                else:
                    for i in range(k-1):
                        answer.append(1)
                    answer.append(n-(k-1))
                    return(" ".join(list(map(lambda x: str(x),answer)))) 
                    
        if (n % 2 == 1) & (k % 2 == 0):
            return("NO")
        if (n % 2 == 1) & (k % 2 == 1):
            for i in range(k-1):
                answer.append(1)
            answer.append(n-(k-1))
            return(" ".join(list(map(lambda x: str(x),answer)))) 
    
def solve(n, k):
    if k > n:
        return("NO")
    else:
        if (k % 2 == 0) & (n % 2 == 1):
            return("NO")
        else:
            if assemble(n,k) == "NO":
                return "NO"
            else:
                return "\n".join(["YES",assemble(n,k)])
        
t = int(input())
answers = []
for i in range(t):
    n, k = to_list(input())
    answers.append(solve(n,k))
print("\n".join(answers))