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:

import sys

def solve(x, y):
    if (x == y):
        print ('YES')
        print('1 '* y)
    elif(y == 1):
        print('YES')
        print(x)

    elif(x < y or (x % 2 != 0 and y % 2 == 0) or (x - y == 1)):
        print('NO')

    elif((x % 2 != 0 and y % 2 != 0) or (x % 2 == 0 and y % 2 == 0)):
        print('YES')
        print(('1 ' * (y -1)).strip(), x - (y - 1))

    elif(x % 2 == 0 and y % 2 != 0):
        if x - ((y - 1) * 2) <= 0:
            print('NO')
        else:
            print('YES')
            print(('2 ' * (y - 1)).strip(), x - ((y - 1) * 2))


def main():

  n_cases = None
  for line in sys.stdin:
      if not n_cases:
          n_cases = line
          continue
      line = line.strip()
      line = line.rstrip()
      line = line.split(" ")
      x = int(line[0])
      y = int(line[1])
      solve(x , y)

main()