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())):
    n,k=map(int,input().split())
    a=[1 for _ in range(k-1)]
    c=0
    fuck=sum(a)
    if (n-fuck)>0 and (n-fuck)%2==1:
        c=1
        print("YES")
        a.append(n-fuck)
        for i in a:
            print(i,end=" ")
        print()
        
    else:
        b=[2 for _ in range(k-1)]
        duck=sum(b)
        if (n-duck)>0 and (n-duck)%2==0:
            c=1
            b.append(n-duck)
            print("YES")
            for i in b:
                print(i,end=" ")
            print()
            
    #print(a,fuck)
    if c==0:
        print("NO")