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:
for _ in range(int(input())):
    
    solved = False
    n, k = list(map(int, input().split()))
    for i in range(1, 3):
        x1 = i
        x2 = n - x1*(k - 1)
        if(x1*(k-1) + x2 == n) and (x1%2 == x2%2) and(x1 > 0) and (x2 > 0):
            print("YES")
            print((str(x1) + ' ') * (k - 1) + str(x2))
            solved = True
            break
        else:
            x1 = str(n // k + 1)
            x2 = str(n - (k - 1)*(n // k + 1))
            if(x1*(k-1) + x2 == n) and (x1%2 == x2%2) and(x1 > 0) and (x2 > 0):
                print("YES")
                print((str(x1) + ' ') * (k - 1) + str(x2))
                solved = True
                break
                
    if not(solved):
        print("NO")