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:
test = int(input())
test_arr = []
for _ in range(test):
    n,k = map(int,input().split(' '))
    n_ = n%2
    k_ = k%2
    if n_!=0 and k_==0:
        test_arr.append(('NO',[]))
        continue
    d = k-1
    
    d = k-1
    if n_==0:
        if k_==0:
            s = n-int(d*1)
            if s>0:
                arr = [1]*d
                arr.append(s)
                test_arr.append(('YES',arr))
            else:
                test_arr.append(('NO',[]))
        else:
            s = n-int(d*2)
            if s>0:
                arr = [2]*d
                arr.append(s)
                test_arr.append(('YES',arr))
            else:
                test_arr.append(('NO',[]))
    else:
        s = n-int(d*1)
        if s>0:
            arr = [1]*d
            arr.append(n-int(d*1))
            test_arr.append(('YES',arr))
        else:
            test_arr.append(('NO',[]))

for t in test_arr:
    print(t[0])
    if len(t[1])>0:
        for i in t[1]:
            print(i,end=' ')
        print('')