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 i in range(int(input())):
    a, k = input().split(); k = int(k)
    b = int(a); lis1 = []; lis2 = []
    x = b
    x1 = b
    b1 = b

    for i in range(k):
        if i == (k-1):
            w = x - sum(lis1)
            if w>0 and w%2==0:
                lis1.append(x - sum(lis1))
        else:
            b = b - 2
            lis1.append(2)

    for i in range(k):
        if i == (k-1):
            w1 = x1 - sum(lis2)
            if w1>0 and w1%2!=0:
                lis2.append(x1 - sum(lis2))
        else:
            b1 = b1 - 1
            lis2.append(1)

    if(sum(lis1)==x and len(lis1)==k):
        print("YES")
        print(*lis1,sep=' ')
    elif sum(lis2)==x1 and len(lis2)==k:
        print("YES")
        print(*lis2,sep=' ')
    else:
        print("NO")