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:
# Note: When I encountered this problem during the virtual contest, I was stumped because I couldn't figure out how to break it down into a simple and easy to understand solution. However, upon watching the beginning of a YouTube video that simplified the problem, I was able to code up this solution.
def sameParitySummands(num: int, num_of_summands: int) -> None:

    if (num < num_of_summands):
        print("NO")
        return

    summands = []

    base = int(num/num_of_summands)

    for i in range(num_of_summands):
        summands.append(base)
    summands[0] += num % num_of_summands

    odd_count = 0
    even_count = 0
    for number in summands:
        if (number % 2):
            odd_count += 1
        else:
            even_count += 1

    if (odd_count == 0 or even_count == 0):
        print("YES")
        for number in summands:
            print(number, end=" ")
        print()
        return
    else:
        if (even_count % 2 == 0):
            for i in range(len(summands)):
                if (summands[i] % 2 == 0):
                    summands[i] -= 1
                    continue_loop = True
                    j = i + 1
                    while (continue_loop and j < len(summands)):
                        if (summands[j] % 2 == 0):
                            summands[j] += 1
                            continue_loop = False
                        j += 1
            for number in summands:
                if (number % 2 == 0):
                    print("NO")
                    return
            print("YES")
            for num in summands:
                print(num, end=" ")
            print()
            return
        elif (odd_count % 2 == 0):
            for i in range(len(summands)):
                if (summands[i] % 2 and summands[i] - 1 != 0):
                    summands[i] -= 1
                    continue_loop = True
                    j = i + 1
                    while (continue_loop and j < len(summands)):
                        if (summands[j] % 2):
                            summands[j] += 1
                            continue_loop = False
                        j += 1
            for number in summands:
                if (number % 2):
                    print("NO")
                    return
            print("YES")
            for num in summands:
                print(num, end=" ")
            print()
            return
        else:
            print("NO")
            return

test_cases = int(input())

for i in range(test_cases):
    inputs = input().split()
    sameParitySummands(int(inputs[0]), int(inputs[1]))