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:
k = int(input())

a = []
for i in range(0, k):
    num1, num2 = [int(x) for x in input().split()]
    if num2 > num1:
        num1 = 3
        num2 = 2
    a.append([num1, num2])

for i in a:
    num1, num2 = i
    arr = []
    odd_index = []
    even_index = []
    for j in range(0, num2):
        arr.append(int(num1/num2))
        if j == num2 - 1:
            arr[-1] = arr[-1] + (num1 % num2)
        even_index.append(j) if arr[j] % 2 == 0 else odd_index.append(j)
    if len(odd_index) == 0 or len(even_index) == 0:
        print("YES")
        print(*arr)
    elif len(odd_index) == len(even_index):
        print("NO")
    elif len(odd_index) % 2 == 0 and arr[0] != 1:
        for k in range(0, int(len(odd_index)/2)):
            arr[odd_index[k]] += 1
            arr[odd_index[len(odd_index) - 1 - k]] -= 1
        print("YES")
        print(*arr)
    elif len(even_index) % 2 == 0:
        for k in range(0, int(len(even_index)/2)):
            arr[even_index[k]] += 1
            arr[even_index[len(even_index) - 1 - k]] -= 1
        print("YES")
        print(*arr)
    else:
        print("NO")