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
input = sys.stdin.readline

def solve(n, k):
	if k > n:
		print("NO")
		return

	res = [n//k for _ in range(k)]
	rem = n%k
	if rem > 0:
		if rem%2 == 1:
			for ii in range(k):
				res[ii] -= 1
				if res[ii] == 0:
					print("NO")
					return
				rem += 1
		if rem%2 == 1:
			print("NO")
			return
		for ii in range(k):
			if rem > 0:
				res[ii] += 2
				rem -= 2
			else:
				break

	print("YES")
	print(" ".join(map(str, res)))

if __name__ == "__main__":
	t = int(input())
	for _ in range(t):
		[n, k] = map(int, input().split())
		solve(n, k)

'''
3 3 3 sisa 1
2 2 2 sisa 4
'''