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 collections

# if (n % 2 != 0 and k % 2 == 0) or k > n:
#     return [False, []]

# quotient = n // k
# remainder = n % k

# print("quotient: {}".format(quotient))
# print("remainder: {}".format(remainder))

# if quotient & 1 ^ remainder & 1:
#     return [False, []]

# if remainder:
#     newQuotient = quotient + 1
# else:
#     return [quotient for _ in range(k)]


def solve(n, k):
    if (n % 2 != 0 and k % 2 == 0) or k > n:
        return [False, []]

    oneChoice, secondChoice = [], []

    if (n % 2 != 0 and k % 2 != 0) or (n % 2 == 0 and k % 2 == 0):
        oneChoice = [1 for _ in range(k-1)] + [n-(k-1)]

    if ((n % 2 == 0 and k % 2 == 0) or (n % 2 == 0 and k % 2 != 0)):
        secondChoice = [2 for _ in range(k-1)] + [n-2*(k-1)]

    if sum(oneChoice) == n and oneChoice[-1] > 0:
        return [True, oneChoice]
    elif sum(secondChoice) == n and secondChoice[-1] > 0:
        return [True, secondChoice]
    else:
        return [False, []]


t = int(input().strip())
# [n,m] = list(map(int, input().strip().split()))

for i in range(t):
    [n, k] = list(map(int, input().strip().split()))

    res, arr = solve(n, k)

    if res:
        print("YES")
        print(" ".join(map(str, arr)))
    else:
        print("NO")