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:
from sys import stdin, stdout
import collections

t = int(input())

def solve(n, k):
    if k > n:
        print('NO')
        return

    if n % k == 0:
        print('YES')
        print(' '.join([str(n // k)] * k))
        return

    if n % 2 == 1 and k % 2 == 0:
        print('NO')
        return

    if k == 1:
        print('YES')
        print(n)
        return

    if n % 2 == 0:
        ans = []

        ans += ['2'] * (k-1)
        nx = n - (k-1)*2

        if nx <= 1 or nx % 2 == 1:
            pas = []

            pas += ['1'] * (k-1)
            x = n - k + 1

            if x <= 0 or x % 2 == 0:
                print('NO')
                return

            pas += [str(x)]

            print('YES')
            print(' '.join(pas))
            return

        ans += [str(nx)]

        print('YES')
        print(' '.join(ans))
        return

    if n % 2 == 1 and k % 2 == 1:
        ans = []

        ans += ['1'] * (k-1)
        nx = n - k + 1

        if nx <= 0:
            print('NO')
            return

        ans += [str(nx)]

        print('YES')
        print(' '.join(ans))
        return

    print('NO')
    return

for i in range(t):
    n, k = list(map(int, stdin.readline().split()))
    solve(n, k)

"""
10
10 3
100 4
8 7
97 2
8 8
3 10
5 3
1000000000 9
10 5
10 6
"""