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 
# sys.stdin = open('input.txt', 'r')
# sys.stdout = open('output.txt', 'w')
mod = int(1e9)+7
def ip():
	return int(input())
def Ip():
	return map(int, input().split())

for _ in range (0, int(input())):
	n,k = Ip()
	l = []
	if n<k:
		print ("NO")
	else:
		if n%2==1:
			if k%2==0:
				print ("NO")
			else:
				print("YES")
				for i in range (0,k-1):
					print (1, end = " ")
				print (n-k+1, end = " ")
				print()
		else:
			if k%2==0:
				print("YES")
				for i in range (0,k-1):
					print (1, end = " ")
				print (n-k+1, end = " ")
				print()
			else:
				if n<(2*k):
					print ("NO")
				else:
					print("YES")
					for i in range (0,k-1):
						print (2, end = " ")
					print (n-(2*(k-1)), end = " ")
					print()