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 < k:
        print("NO")
        continue

    if n%k == 0:
        print("YES")
        for i in range(k):
            print(n//k,end = " ")

        print('')
        continue

    div = n//k
    rem = n%k
    if ((div % 2 == 0)and(rem%2 == 0))or((div % 2 != 0)and(rem%2 == 0)):
        print("YES")
        for i in range(k):
            if i == k-1:
                print(div+rem, end=" ")

            else:
                print(div, end=" ")

        print('')
        continue

    else:
        if div == 1:
            print("NO")
            continue

        if (k-1)%2 != 0:
            print("NO")
            continue

        else:
            print("YES")
            for i in range(k-1):
                if i%2 == 0:
                    print(div - 1, end=" ")

                else:
                    print(div+1, end=" ")

            print(div+rem,end = '')
            print('')
            continue