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:
t=int(input())
def fun(n,k):
    odd=[1 for i in range(k-1)]
    if (n-k+1)%2==1:
        odd.append(n-k+1)
    else:
        odd=[]
    even=[2 for i in range(k-1)]
    if (n-2*k+2)%2==0:
        even.append(int(n-2*k+2))
    else:
        even=[]
    if len(odd)==0 and len(even)==0:
        print("NO")
    else:
        flo=0
        fle=0
        if len(even)==0:
            for i in odd:
                if i<=0:
                    flo+=1
                    break
            if flo:
                print("NO")
            else:
                print("YES")
                print(*odd,sep=" ")
        elif len(odd)==0:
            for i in even:
                if i<=0:
                    fle+=1
                    break
            if fle:
                print("NO")
            else:
                print("YES")
                print(*even,sep=" ")
        else:
            flo=0
            fle=0
            for i in even:
                if i<=0:
                    fle+=1
                    break
            for i in odd:
                if i<=0:
                    flo+=1
                    break
            if fle==1 and flo==1:
                print("NO")
            elif flo:
                print("YES")
                print(*even,sep=" ")
            else:
                print("YES")
                print(*odd,sep=" ")
while t:
    t-=1
    n,k=map(int,input().split())
    fun(n,k)