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:
"https://codeforces.com/contest/1328/problem/A"
import collections, heapq, itertools, math
groupby = itertools.groupby
rs  = lambda: input()
ri  = lambda: int(input())
rm  = lambda: map(int, input().split())
rai = lambda: [int(x) for x in input().split()]


def solve(n, k):
    ans = []
    ans2 = []
    c1 = c2 = k
    m = l = n
    while c1 > 1:
        ans.append(1)
        m -= 1
        c1 -= 1
    ans.append(m)
    
    while c2 > 1:
        ans2.append(2)
        l -= 2
        c2 -= 1
    ans2.append(l)
    

    if ans[-1] > 0 and ans[-1] % 2 and len(ans) == k:
        return True, ans
    elif ans2[-1] > 0 and ans2[-1] % 2 == 0 and len(ans2) == k:
        return True, ans2
    else: return False, []

for t in range(ri()):
    n, k = rm()
    a, b = solve(n, k)
    #print("---op---")
    if a:
        print('YES')
        print(*b)
    else:
        print('NO')
    #print('\n')