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:
tt = int(input())

while tt:
    n,k = [int(x) for x in input().split()]
    if n < k:
        print("NO")
    elif n%2 != 0 and k%2 == 0:
        #n is odd and k is even
        print("NO")
    elif n%2 != 0 and k%2 !=0:
        #n is odd and k is odd
        ans = ""
        for i in range(0,k-1):
            ans += "1 "
        ans += str(n-k+1)
        print("YES")
        print(ans)
    elif n%2 == 0:
        #if n is even
        if k%2==0:
            #if k is even
            ans = ""
            for i in range(0, k - 1):
                ans += "1 "
            ans += str(n - k + 1)
            print("YES")
            print(ans)
        else:
            if n < 2*k:
                print("NO")
            else:
                ans = ""
                for i in range(0, k - 1):
                    ans += "2 "
                ans += str(n - (2*(k-1)))
                print("YES")
                print(ans)
    tt-= 1