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 even1(n,k):
    li1=[]
    if((n//2)//k>0):
           value=(n//2)//k
           for i in range(1,k):
                  li1.append(2*value)
           value2=sum(li1)
           if((n-value2)%2==0):
                     li1.append(n-value2)
    return li1
def odd(n,k):
      li1=[]
      if(n//k>0):
          value=n//k
          if(value%2==0):
                value=value-1
          for i in range(1,k):
                   li1.append(value)
          value2=sum(li1)
          if((n-value2)%2!=0):
                     li1.append(n-value2)
      return li1                 
testcase=int(input())
for i in range(testcase):
        n,k=map(int,input().split())
        li1=even1(n,k)
        bool2=True
        for i in range(len(li1)):
               if(li1[i]%2!=0):
                       bool2=False
        if(bool2==True and sum(li1)==n):
                 print("YES")
                 print(*li1)
        else:
            li1=odd(n,k)
            bool2=True
            for i in range(len(li1)):
                   if(li1[i]%2==0):
                           bool2=False
            if(bool2==True and sum(li1)==n):
                     print("YES")
                     print(*li1)
        
            else:
                print("NO")