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 sys

def read_int():
    return int(sys.stdin.readline())

def read_ints():
    return list(map(int, sys.stdin.readline().split()))


t = read_int()
# t = 8

# input1 = [(10, 3), (100, 4), (8, 7), (97, 2), (8, 8), (3, 10), (5, 3), (1000000000, 9)]
for j in range(t):
    n, k = read_ints()
    # n, k = input1[j]

    if n < k:
        print('NO')
        continue

    # делим поровну
    chastnoe = n // k
    ostatok = n % k
    lst = [chastnoe] * k
    if ostatok == 0:
        print('YES')
        print(*lst)
    elif ostatok % 2 == 0:
        for j in range(int(ostatok/2)):
            lst[j] += 2
        print('YES')
        print(*lst)
    elif ((k - ostatok) % 2 == 0 and chastnoe > 1):
        # меняем чётность всем

        for j in range(len(lst)):
            if j >= k-ostatok or j % 2:
                lst[j] += 1
            else:
                lst[j] -= 1
        print('YES')
        print(*lst)

    else:
        print('NO')