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());sol=[];temp=[]
for i in range(t):
    main=list(map(int,input().split()))
    if(main[1]>main[0]):
        sol.append(0)
    else:
        if(main[0]%main[1]==0):
            for y in range(main[1]):
                temp.append(main[0]//main[1])
            sol.append(temp)
        else:
            if(main[0]%2==0 and main[1]%2!=0):#(Par) con impar
                if(main[0]-(main[1]-1)*2>0):
                    for j in range(main[1]-1):
                        temp.append(2)
                    temp.append(main[0]-(main[1]-1)*2)
                    sol.append(temp)
                else:
                    sol.append(0)
            elif((main[0]%2==0 and main[1]%2==0) or (main[0]%2!=0 and main[1]%2!=0)) :#PAR CON PAR
                if(main[0]-(main[1]-1)>0):

                    for x in range(main[1]-1):
                        temp.append(1)
                    temp.append(main[0]-(main[1]-1))
                    sol.append(temp)
                else:
                    sol.append(0)
            elif(main[0]%2!=0 and main[1]%2==0):
                sol.append(0)
    temp=[]
for xxx in sol:
    if(xxx==0):
        print('NO')
    else: 
        print('YES')
        print(*xxx)