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:
t = int(input())
ls = []
ls2 = []        
for k in range(t):
    n,k = map(int,input().split())
    ls.append(n)
    ls2.append(k)
for i in range(t):
    a = ls[i]
    b = ls2[i]
    if a%b == 0:
        print("YES")
        for j in range(b):
            print(int(a/b),end=' ')
        print(' ')
    else:
        div = int(a/b)
        n1 = div
        n2 = a-(n1*(b-1))
        if n1%2 == n2%2 and n1>0 and n2>0:
            print("YES")
            for j in range(b-1):
                print(n1,end=' ')
            print(n2)
        elif n2 - (b-1) > 0 and (n1+1)%2 == (n2-(b-1))%2 and n1+1>0 and (n2-(b-1)) >0:
            print("YES")
            for j in range(b-1):
                print(n1+1,end=' ')
            print(n2-(b-1))
        elif n1>1 and (n2+b-1)%2 == (n1-1)%2 and (n2+b-1)>0:
            print("YES")
            for j in range(b-1):
                print(n1-1,end=' ')
            print(n2+(b-1))
        else:
            print("NO")