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:
# Author : Mradul Tiwari

import heapq as hp
import collections
import bisect
import math
import re


def unpack(func=int):
    return map(func, input().split())


def l_unpack(func=int):
    """list unpack"""
    return list(map(func, input().split()))


def s_unpack(func=int):
    """sorted list unpack"""
    return sorted(map(func, input().split()))


def ml_unpack(n):  # multiple line unpack
    """list of n integers passed on n line, one on each"""
    return [int(input()) for i in range(n)]


def range_n():
    return range(int(input()))


def counter(a):
    d = {}
    for x in a:
        if x in d:
            d[x] += 1
        else:
            d[x] = 1
    return d


def getint():
    return int(input())


def setbits(x):
    count = 0
    while x:
        x = x & (x - 1)
        count += 1
    return count


def main():
    for _ in range_n():
        n, k = unpack()
        n1 = n - k + 1
        if n1 > 0 and n1 & 1:
            print('YES')
            for i in range(k - 1):
                print(1, end=' ')
            print(n1)
            continue
        n2 = n - 2 * (k - 1)
        if n2 > 0 and n2 % 2 == 0:
            print('YES')
            for i in range(k - 1):
                print(2, end=' ')
            print(n2)
            continue
        print('NO')


main()