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 sameparity(a, b):
  arr = []
  count = 0
  if(a==b):
    arr = [1]*a
    return arr
  if(a%2==0):
    if(b%2==0):
      while(b!=1):
        arr.append(1)
        b-=1
        count +=1
        if(count==a):
          return "NO"
    else:
      while(b!=1):
        arr.append(2)
        b-=1
        count +=2
        if(count==a):
          return "NO"
    arr.append(a-count)
      
  else:
    if(b%2==0):
      return "NO"
    else:
      while(b!=1):
        arr.append(1)
        b-=1
        count +=1
        if(count==a):
          return "NO"
    arr.append(a-count)
      
      
  return arr
    

test = int(input())
for i in range(test):
  a, b = map(int, input().split())
  z = sameparity(a, b)
  if(z=='NO'):
    print(z)
  else:
    print("YES")
    print(*z)