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

input = stdin.readline


def main():
    test = int(input())

    for t in range(test):
        # n = int(input())
        l = [int(i) for i in input().split(" ")]
        n = l[0]
        k = l[1]
        # l = [int(i) for i in input().split(" ")]
        l = []
        flag = True

        if k > n:
            print("NO")
        else:
            if n % 2 == 0 and k % 2 == 0:
                c = 0
                while k > 1:
                    l.append(1)
                    c += 1
                    k -= 1
                l.append(n - c)
                if n-c <=0 :
                    flag = False
            elif n % 2 == 0 and k % 2 != 0:
                c = 0
                while k > 1:
                    l.append(2)
                    c += 2
                    k -= 1
                l.append(n - c)
                if n-c <= 0:
                    flag = False
            elif n % 2 != 0 and k % 2 == 0:
                flag = False
            else:
                c = 0
                while k > 1:
                    l.append(1)
                    c += 1
                    k -= 1
                l.append(n - c)
                if n - c <= 0:
                    flag = False

            if flag:
                print("YES")
                for i in l:
                    print(i, end=' ')
                print()
            else:
                print("NO")


main()