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:
class A:

    def solve(self):
        t = int(input())
        for i in range(t):
            n = list(map(int, input()))
            round_numbers = list(map(lambda x: x[0] * 10**x[1], filter(lambda x: x[0] > 0,
                                                                   zip(n, reversed(list(range(len(n))))))))
            print(len(round_numbers))
            print(" ".join(map(str, round_numbers)))

class B:

    def solve(self):
        t = int(input())
        for p in range(t):
            in_list = list(map(int, input().split(" ")))
            n, k = in_list[0], in_list[1]
            if k % 2 == 1:
                if n % 2 == 0:
                    first_term = n - (k - 1) * 2
                    if first_term <= 0:
                        print("NO")
                        continue
                    print("YES")
                    print(" ".join([str(first_term)] + ["2" for x in range(k - 1)]))
                else:
                    first_term = n - (k - 1)
                    if first_term <= 0:
                        print("NO")
                        continue
                    print("YES")
                    print(" ".join([str(first_term)] + ["1" for x in range(k - 1)]))
            else:
                if n % 2 == 0:
                    first_term = n - (k - 1)
                    if first_term <= 0:
                        print("NO")
                        continue

                    if first_term % 2 == 1:
                        print("YES")
                        print(" ".join([str(first_term)] + ["1" for x in range(k - 1)]))
                        continue

                    first_term = n - (k - 1) * 2

                    if first_term <= 0:
                        print("NO")
                        continue

                    if first_term % 2 == 0:
                        print("YES")
                        print(" ".join([str(first_term)] + ["2" for x in range(k - 1)]))
                    else:
                        print("NO")
                else:
                    print("NO")

B().solve()