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 numpy as np
# # # a = np.array([[1,2,3],[4,5,6]])
# # # print(a.ndim)
# # # f = open("hello.txt","w")
# # # f.write("Hello Darkness my old friend!")
# # # f.close()

# # # f = open("hello.txt","a")
# # # f.write("\nHello Darkness my old friend!")
# # # f.close()

# # # f = open("hello.txt","r")
# # # for x in f:
# # # 	print(x)

# # # import os
# # # os.remove("hello.txt")
# # # k = int(input())

# # # if not type(k) is int:
# # # 	raise TypeError("Integer daalna hai :|")
# # # else:
# # # 	print("Correct :)")

# # # try:
# # # 	k = int(input())
# # # except ValueError:
# # # 	raise TypeError("Integer Daalna")
# # # else:
# # # 	print("Correct")
# # x = "hello"

# # if not type(x) is int:
# #   raise TypeError("Only integers are allowed")
# # import math
# for _ in range(int(input())):
# 	n = int(input())
# 	k = n
# 	l =[]
# 	for i in range(math.floor(math.log(k, 10)+1)):
# 		r = n%10
# 		if(r!=0):
# 			l += [(r*pow(10,i))]
# 		n = n//10
# 	print(len(l))
# 	for x in l:
# 		print(x,end=" ")

# # def z(n,k):
# # 	if(k<n):
# # 		return(k)
# # 	else:
# # 		s = k//n
# # 		if((k + s)//n == s):
# # 			return(k + s)
# # 		else:
# # 			m = s*n
# # 			k = k - s*n + s
# # 			return(m + z(n,k))

# # for _ in range(int(input())):
# # 	n,k = map(int,input().split())
# # # 	print(z(n,k))
# for _ in range(int(input())):
# 	n = int(input())
# 	l = []
# 	for i in range(4):
# 		if(n%10 != 0):
# 			l += [n%10 * pow(10,i)]
# 		n = n//10
# 		if(n==0):
# 			break
# 	print(len(l))
# 	for x in l:
# 		print(x,end=" ")
def z(n,k,x):
	if(k*x > n):
		print("NO")
		return
	else:
		l = []
		for _ in range(k-1):
			l+=[x]
		l+=[n - x*k + x]
	print("YES")
	for x in l:
		print(x,end=" ")
	return

for _ in range(int(input())):
	n,k = map(int,input().split())
	if(k%2==0):
		if(n%2==0):
			z(n,k,1)
		else:
			print("NO")
	else:
		if(n%2==0):
			z(n,k,2)
		else:
			z(n,k,1)