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:
for _ in range(int(input())):
	n, k = map(int, input().split())
	if n < k:
		print("NO")
	elif n % k == 0:
		print("YES")
		li = [n // k] * k
		print(*li, sep = " ")
	else:
		x = (n // k)
		li = [x] * k
		y = x - 1
		li2 = [y] * k
		if x % 2 == (x + (n - (k * x))) % 2:
			li[0] += (n - (k * x))
			print("YES")
			print(*li, sep = " ")
		elif y != 0 and y % 2 == (y + (n - (k * y))) % 2:
			li2[0] += (n - (k * y))
			print("YES")
			#print(y)
			print(*li2, sep = " ")
		else:
			print("NO")