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 PYTHON):

Solution:
from __future__ import division
from __future__ import print_function


import itertools

input = raw_input
range = xrange

filter = itertools.ifilter
map = itertools.imap
zip = itertools.izip


def read_int():
    return int(input())


def read_ints():
    return list(map(int, input().split(' ')))


def read_str():
    return input()


def read_strs():
    return input().split(' ')


def solve():
    n, k = read_ints()

    s = 0
    for i in range(k - 1):
        s += 1

    if n - s > 0 and (n - s) % 2 == 1:
        print("YES")
        for i in range(k - 1):
            print(1, end=" ")
        print(n - s)
        return

    s = 0
    for i in range(k - 1):
        s += 2

    if n - s > 0 and (n - s) % 2 == 0:
        print("YES")
        for i in range(k - 1):
            print(2, end=" ")
        print(n - s)
        return

    print("NO")



t = read_int()
for case in range(t):
    solve()