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())
while t>0:
    t-=1
    N,K = map(int,input().split())
   
    
    if(N%2==1 ):
        
        if(K%2==0 or N<K):
            print( "NO" )
            continue
        
        else:
        
            print( "YES") 
            K-=1;
            while(K>0):
                K-=1
                print("1",end=" ");
                N-=1;
            
            print(N) 
        
    else:
            
        if((K%2==1 and N<K*2 )or(K%2==0 and N<K)):
        
            print( "NO")
            continue
        
        elif (K%2==1):
        
            print("YES") 
            K-=1;
            while(K>0):
                K-=1
                print("2",end=" ")
                N-=2;
            
            print( N)
        
        else:
        
            print( "YES" )
            K-=1;
            while(K>0):
                K-=1
                print( "1",end=" ");
                N-=1;
            
            print( N )