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 parity(n,k):
    l=[]
    if n<k:
        return "NO",[]
    if n%2!=0:
        if k%2==0:
            ans="NO"
            return ans,l
        l=[1]*(k-1)
        l.append(n-k+1)
        ans="YES"
        return ans,l
    elif n%2==0:
        if n//2 >= k:
            l=[2]*(k-1)
            l.append(n-2*(k-1))
            ans="YES"
            return ans,l
        elif k%2==0:
            l=[1]*(k-1)
            l.append(n-k+1)
            ans="YES"
            return ans,l
        else:
            ans="NO"
            return ans,l
            
T=int(input())
for i in range(T):
    n,k=[int(j) for j in input().split()]
    a,b=parity(n,k)
    if a=="NO":
        print(a)
    else:
        print(a)
        for j in b:
            print(j,end=" ")
        print()