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:
from sys import stdin




def solve():
    n,k = [int(i) for i in stdin.readline().split()]
    l = n
    m = n
    A = ''
    for i in range(k - 1):
        if n <= 0: break
        n -= 2
        A += " 2"
    # print("m : {} | n: {}".format(m,n))
    if n > 0 and n % 2 == 0:
        A += " " + str(n)
        print("YES")
        print(A.strip())
        return 0
    A = ''
    for i in range(k - 1):
        if l <= 0:
            print("NO")
            return 0
        l -= 1
        A += " 1"
    if l > 0 and l % 2 == 1:
        A += " " + str(l)
        print("YES")
        print(A.strip())
        return 0
    print("NO")
    return 0

t = int(input())
for i in range(t):
    k = solve()