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:
testy = int(input(""))
results = []
def wynik(n, k):
    result = []
    m = n
    l = k
    if n % 2 == 1 and k % 2 == 0:        
        result.append("NO")
        return result
    elif n % 2 == 1 and k % 2 == 1 and n >= k:       
        result.append("YES")
        while l > 1:
            result.append(1)
            m -= 1
            l -= 1
        result.append(n - k + 1)
        return result
    elif n % 2 == 0 and n >= k *2:
        result.append("YES")
        while l > 1:
            result.append(2)
            m -= 2
            l -= 1
        result.append(n - k * 2 + 2)
        return result  
    elif n % 2 == 0 and k % 2 == 0 and n >= k:
        result.append("YES")
        while l > 1:
            result.append(1)
            m -= 1
            l -= 1
        result.append(n - k + 1)
        return result 
    else:
        result.append("NO")
        return result 

for i in range(0 , testy):
    wejscie = input("")
    n = int(wejscie.split()[0])
    k = int(wejscie.split()[1])
    results.append(wynik(n, k))    
for result in results:
    for czesc in result:
        if type(czesc) == str:
            print(czesc)
        else:
            print(czesc,end ="")
            print(" ", end ="")
    if result[0] == "YES":
        print("")