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:
def odd(n, k):
    h = n - k
    if h < 0 or h % 2 != 0:
        return None
    h = h // 2
    c = h // k
    d = h % k
    arr = [c] * k
    arr[-1] += d
    arr = list(map(lambda x: 2 * x + 1, arr))
    return arr

def even(n, k):
    if n % 2 != 0:
        return None
    h = n // 2
    c = h // k
    if h == 0 or c == 0: 
        return None
    d = h % k
    arr = [c] * k
    arr[-1] += d
    arr = list(map(lambda x: 2 * x, arr))
    return arr

def _odd(n, k):
    nn = n - (k - 1)
    if nn > 0 and nn % 2 == 1:
        return '1 ' * (k - 1) + str(nn)

def _even(n, k):
    nn = n - 2 * (k - 1)
    if nn > 0 and nn % 2 == 0:
        return '2 ' * (k - 1) + str(nn)
    return None

t = int(input())
for _ in range(t):
    n, k = tuple([int(e) for e in input().split()])
    s1 = _odd(n, k)
    s2 = _even(n, k)
    if not s1 and not s2:
        print('NO')
        continue
    print('YES')
    if s1:
        print(s1)
    else:
        print(s2)

# t = int(input())
# for _ in range(t):
#     n, k = tuple([int(e) for e in input().split()])
#     if n % 2 == 1 and k % 2 == 0:
#         print('NO')
#         continue
#     haveSolution = False
#     arr1 = odd(n, k)
#     if arr1: haveSolution = True
#     arr2 = even(n, k)
#     if arr2: haveSolution = True
#     if haveSolution:
#         print('YES')
#         arr = arr1
#         if arr2:
#             arr = arr2
#         print(' '.join(list(map(str, arr))))
#     else:
#         print('NO')