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 SameParitySummands():
    length = int(input())
    numData = [None for _ in range(length)]
    for i in range(length):
        numData[i] = input()
        numData[i] = numData[i].split(' ')
    result = []
    
    for elem in numData:
        data = int(elem[0])
        length = int(elem[1])
        terms = findTerms(data, length)
        result.append(terms)
    
    for elem in result:
        print(elem[0])
        if elem[0] == 'YES':
            for term in elem[1]:
                print(term, end="\t")
            if elem != result[-1]:
                print()

def findTerms(data, length):
    if length == 1:
        return ['YES', [data]]
    elif (data - length) // 2 * 2 == data - length and data - length >= 0:
        minimum = (data - length) // (2 * length) * 2 + 1
        addNum = [minimum for _ in range(length)]
        increasement = (data - minimum * length)
        addNum[0] += increasement
        return ['YES', addNum]
    elif (data - 2 * length) // 2 * 2 == data - 2 * length and data - 2 * length >= 0:
        minimum = (data - 2 * length) // (2 * length) * 2 + 2
        addNum = [minimum for _ in range(length)]
        increasement = (data - minimum * length)
        addNum[0] += increasement
        return ['YES', addNum]
    else:
        return ['NO', []]

SameParitySummands()