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:
for _ in range(int(input())):
    n, k = map(int, input().split())
    if n==0 or k==0:
        print("NO")
        continue
    if n < k:
        print("NO")
        continue
    if n == k:
        print("YES")
        for i in range(n):
            print(1, end=' ')
        print()
        continue
    n_even = (n%2==0)
    k_even = (k%2==0)
    n_odd = (n%2==1)
    k_odd = (k%2==1)
    if n_odd and k_odd:
        Sum=0
        print("YES")
        for x in range(k-1):
            Sum+=1
            print(1, end=' ')
        print(n-Sum)
        continue
    if n_even and k_odd:
        if 2*(k-1) >= n-1:
            print("NO")
        else:
            print("YES")
            Sum=0
            for x in range(k-1):
                print(2, end=' ')
                Sum+=2
            print(n-Sum)
        continue
    if n_odd and k_even:
        # print("HERE it is")
        print("NO")
        continue
    if n_even and k_even:
        print("YES")
        Sum=0
        for x in range(k-1):
            print(1, end=' ')
            Sum+=1
        print(n-Sum)
        continue