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:
"""
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 / ___|___   __| | ___|  ___|__  _ __ ___ ___  ___
| |   / _ \ / _` |/ _ \ |_ / _ \| '__/ __/ _ \/ __|
| |__| (_) | (_| |  __/  _| (_) | | | (_|  __/\__ \
 \____\___/ \__,_|\___|_|  \___/|_|  \___\___||___/

"""
"""
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"""

import sys
import math
import collections
import operator as op
from collections import deque
from math import gcd, inf, sqrt, pi, cos, sin
from bisect import bisect_right, bisect_left

#sys.stdin = open('input.txt', 'r')
#sys.stdout = open('output.txt', 'w')

from functools import reduce
from sys import stdin, stdout, setrecursionlimit
setrecursionlimit(2**20)


def factorial(n):
    if n == 0:
        return 1
    return n * factorial(n - 1)


def ncr(n, r):
    r = min(r, n - r)
    numer = reduce(op.mul, range(n, n - r, -1), 1)
    denom = reduce(op.mul, range(1, r + 1), 1)
    return numer // denom  # or / in Python 2


def prime_factors(n):
    i = 2
    factors = []
    while i * i <= n:
        if n % i:
            i += 1
        else:
            n //= i
            factors.append(i)
    if n > 1:
        factors.append(n)
    return len(set(factors))


def isPowerOfTwo(x):
    return (x and (not(x & (x - 1))))


def factors(n):
    return list(set(reduce(list.__add__, ([i, n // i] for i in range(1, int(n**0.5) + 1) if n % i == 0))))


def mod0cnt(n):
    return n // 3


def mod1cnt(n):
    return n // 3 + (n % 3 != 0)


def mod2cnt(n):
    return n // 3 + (n % 3 == 2) + 1

MOD = 1000000007
T = 1
T = int(stdin.readline())
for _ in range(T):
    n, k = list(map(int, stdin.readline().split()))
    # s1 = list(stdin.readline().strip('\n'))
    # n = int(stdin.readline())
    #n, m, x = list(map(int, stdin.readline().split()))
    # s = str(stdin.readline().strip('\n'))
    # s2 = list(stdin.readline().strip('\n'))
    # a = list(map(int, stdin.readline().split()))
    if k > n:
        print('NO')
        continue
    ans = []
    if n % 2 == 1:
        if k % 2 == 0:
            print('NO')
            continue
        else:
            if k - 1 >= n:
                print('NO')
                continue
            else:
                ans = [1] * (k - 1)
                ans = ans + [n - k + 1]
    else:
        if k % 2 == 0:
            if k - 1 >= n:
                print('NO')
                continue
            else:
                ans = [1] * (k - 1)
                ans = ans + [n - k + 1]
        else:
            if 2 * (k - 1) >= n:
                print('NO')
                continue
            else:
                ans = [2] * (k - 1)
                ans = ans + [n - 2 * (k - 1)]
    print('YES')
    print(*ans)