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 same(j):
    if  j[1]>j[0]:
       print("NO")
    elif j[0]%2==0:
       if j[1]%2==0:
           print("YES")
           print("1 "*(j[1]-1)+str(j[0]-j[1]+1))
       else:
           if j[0]-2*j[1]+2>0:
            print("YES")
            print("2 "*(j[1]-1)+str(j[0]-2*j[1]+2))
           else:
            print("NO")     
    else:
       if j[1]%2==0:
           print("NO")
       else:
           print("YES")
           print("1 "*(j[1]-1)+str(j[0]-j[1]+1)) 
t=int(input())
l=[]
for i in range(t):
    n,k=input().split()
    l.append([int(n),int(k)])
for j in l:
    same(j)