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 nltk
# from math import log
# from matplotlib import pyplot as plt
# import numpy as np
# from nltk.corpus import gutenberg as gb
#
# fdist = nltk.FreqDist(gb.words('burgess-busterbrown.txt'))
# l = fdist.most_common(200)
#
# x = np.arange(1, 201, dtype='float_')
# y = x.copy()
# for i, v in enumerate(x):
#     x[i] = 1.0 * log(1 / v)
# for i, v in enumerate(y):
#     y[i] = log(l[i][1])
#
# plt.plot(x, y)
# plt.show()
T = int(input())
while T:
    T -= 1
    n, k = map(int, input().split())
    if k & 1:
        if n & 1:
            if n - k + 1 > 0:
                print("YES")
                print("1 " * (k - 1) + str(n - k + 1))
            else:
                print("NO")
        else:
            r = n - (k - 1) * 2
            if r % 2 == 0 and r > 0:
                print("YES")
                print("2 " * (k - 1) + str(r))
            else:
                print("NO")
    else:
        if n & 1:
            print("NO")
        else:
            if n - k + 1 > 0 and (n - k + 1) % 2 == 1:
                print("YES")
                print("1 " * (k - 1) + str(n - k + 1))
            elif n - (k - 1) * 2 > 0 and (n - (k - 1) * 2) % 2 == 0:
                print("YES")
                print("YES")
                print("2 " * (k - 1) + str(n - (k - 1) * 2))
            else:
                print("NO")