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())
    f = n // k
    arr = []
    temp = 0
    judge = True
    if f == 0:
        print("NO")
        continue
    if n == 1 and k == 1:
        print("YES")
        print(1)
        continue
    if k == 1:
        print("YES")
        print(n)
        continue
    for i in range(k):
        if i == k - 1:
            if (arr[-1] + (n-sum(arr))) % 2 == 1:
                judge = False
            else:
                arr.append(n-sum(arr))
        else:
            arr.append(f)

    if judge == True:
        print("YES")
        for k in range(len(arr)):
            if k == len(arr)-1:
                print(arr[k])
            else:
                print(arr[k], end=' ')
    else:
        f -= 1
        arr = []
        temp = 0
        if f == 0:
            print("NO")
        else:
            for j in range(k):
                if j == k - 1:
                    if (arr[-1] + (n-sum(arr))) % 2 != 1:
                        judge = True
                        arr.append(n-sum(arr))
                    else:
                        pass
                else:
                    arr.append(f)
            if judge == False:
                print("NO")
            else:
                print("YES")
                for l in range(len(arr)):
                    if l == len(arr)-1:
                        print(arr[l])
                    else:
                        print(arr[l], end=' ')