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:
t = int(input())
for _ in range(t):
    fail = False
    (n,k) = tuple(map(int,input().split()))
    if k == 1:
        print("YES")
        print(n)
        continue
    is_n_odd = n % 2
    is_k_odd = k % 2
    if not is_n_odd:
        if is_k_odd:
            if 2*(k-1) <= n-2:
                first = "2"
                to_print = (n-2)//(k-1)
                if to_print % 2 == 1:
                    to_print -= 1
                last = n-2
            else:
                fail = True
        else:
            if k-1 <= n-1:
                first = "1"
                to_print = (n-1)//(k-1)
                if to_print % 2 == 0:
                    to_print -= 1
                last = n-1
            else:
                fail = True

    else:
        if is_k_odd:
            if k-1 <= n-1:
                first = "1"
                to_print = (n-1)//(k-1)
                if to_print % 2 == 0:
                    to_print -= 1
                last = n-1
            else:
                fail = True
        else:
            fail = True

    if not fail:
        to_print = str(to_print)
        print("YES")
        print(first, end=" ")
        for __ in range(k-2):
                print(to_print,end=" ")
        last -= int(to_print) * (k-2)
        print(last)
    else:
        print("NO")