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:
import sys

T = int(sys.stdin.readline())
for _ in range(T):
    n, k = map(int, sys.stdin.readline().split())
    if not n%2 and k%2:
        key = 2
    elif n%2 and not k%2:
        print('NO')
        continue
    elif n%2 and k%2:
        key = 1
    else:
        if n > k*2:
            key = 2
        else:
            key = 1
    result = []
    for count in range(1, k+1):
        if n < 0:
            result = []
            break
        if count == k:
            if n%2 == key%2 and n:
                result.append(n)
            else:
                result = []
            continue
        result.append(key)
        n-=key
    if result:
        print('YES')
        print(*result)
    else:
        print('NO')