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:
"""
- math -
from math import factorial
from math import gcd
from math import pi
large_p = 10**9 + 7
from itertools import accumulate # 累積和
from operator import mul
- other -
from collections import Counter
from itertools import combinations
from itertools import combinations_with_replacement
from itertools import permutations
from operator import itemgetter
from functools import reduce
- list -
from copy import deepcopy
from collections import deque
from heapq import heapify, heappop, heappush
- output -
p2d = lambda x: print(*x, sep="\n")
p2line = lambda x: print(*x, sep=" ")
print(*list1, sep="\n")
- input -
import sys
read = sys.stdin.read
readline = sys.stdin.readline
readlines = sys.stdin.readlines
= map(int, input().split())
= [tuple(map(int, input().split())) for _ in range(n)]
m = map(int, read().split()) /ab = zip(m, m) /for a, b in ab:
ps = [line.split() for line in readlines()] # inputの最後まで読んでしまうので注意。
n, k, *h = map(int, read().split()) # 1行目にnとk,2行目にh0,h1,,,hn
- run -
sys.setrecursionlimit(10**6)
from time import sleep
"""
# ATC04

import sys
read = sys.stdin.read
from math import log10,floor
def main():
    a = int(input())
    for _ in range(a):
        n, k = map(int, input().split())
        if n < k:
            print('NO')
        elif n == k:
            print('YES')
            r = [n // k] * k
            print(*r, sep=' ')
        else:
            p = n / 2
            if p % 1 == 0 and p >= k:
                print('YES')
                print(int((p - k + 1) * 2),end= ' ')
                r = [2] * (k - 1)
                print(*r, sep=' ')
            else:
                p = (n - k) / 2
                if p % 1 == 0:
                    print('YES')
                    print(int(p * 2 + 1), end=' ')
                    r = [1] * (k - 1)
                    print(*r, sep=' ')
                else:
                    print('NO')

if __name__ == '__main__':
    main()

"""
a = (n // k) * 2
        x = n - a
        if x % 2 == 0:
            print('YES')
            r1 = a // k + x
            print(r1, end=' ')
            r2 = [a//k] * (k - 1)
            print(*r2, sep=' ')
        else:
            if x % k == 0:
                print('YES')
                r1 = [a + (n - a // k)] * k
                print(*r1, sep='')
            else:
                print('NO')
"""