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 PYTHON):

Solution:
import sys

def with_even(n,k):
	if (n - (k-1)*2) % 2 == 1 or (n - (k-1)*2) < 2:
		return False, []
	else:
		res = [2] * (k-1) + [n - 2*(k - 1)]
		return True, [str(x) for x in res]

def with_odd(n,k):
	if (n - (k - 1)) % 2 == 0 or (n - (k - 1)) < 1:
		return False, []
	else:
		res = [1] * (k-1) + [n - (k - 1)]
		return True, [str(x) for x in res]

t = int(sys.stdin.readline().strip())
for i in range(t):
	n,k = list(map(int,sys.stdin.readline().strip().split(' ')))
	b,r = with_even(n,k)
	if b:
		print("YES")
		print(' '.join(r))
	else:
		b,r = with_odd(n,k)
		if b:
			print("YES")
			print(' '.join(r))
		else:
			print("NO")