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:

N=int(input())
    
for _ in range(N):
#    n=list(map(str,input()))
    x,y=map(int,input().split())
#    x1,y1=map(int,input().split())
#    a,b,q=map(int,input().split())
    l=[]
#    s=list(map(int,input().split()))
#    
#    l1=[]
#    l2=[]
#    n=int(input())
    if(y>x):
        print("NO")
    else:
        if(x%y==0):
            ans =x//y
            print("YES")
            for i in range(y):
                l.append(ans)
            print(*l)
        else:
            if(x%2==0 and y%2==0):
                print("YES")
                for i in range(y-1):
                    l.append('1')
                l.append(str(x-y+1))
                print(*l)
            elif(x%2!=0 and y%2!=0):
                print("YES")
                for i in range(y-1):
                    l.append('1')
                l.append(str(x-y+1))
                print(*l)
            
            elif(x%2==0 and y%2!=0):
                if(x>=2*y):
                    print("YES")
                    for i in range(y-1):
                        l.append('2')
                    l.append(str(x-2*(y-1)))
                    print(*l)
                else:
                    print("NO")
            else:
                print("NO")