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:
def calcNos(A, N):
    S = sum(A)
    while(S<N):
        if(N-S == len(A) and len(A)%2 == 0):
            for i in range(len(A)//2):
                A[i]+=2
                S+=2
        else:
            A[0]+=2
            S+=2
    return A


T = int(input())
for _ in range(T):
    N, K = map(int, input().split())
    if(N%K == 0):
        print('YES')
        print(' '.join([str(N//K)]*K))
        continue
    if(K > N):
        print('NO')
        continue
    if(N%2 == 1 and K%2 == 0):
        print('NO')
        continue
    if(N%2 == 0 and K%2 == 1):
        init = N//K
        if(init%2 == 1):
            init-=1
    elif(N%2 == 1):
        init = N//K
        if(init%2 == 0):
            init-=1
    else:
        init = N//K
    if(init <= 0):
        init = 1
    A = calcNos([init]*K, N)
    if(sum(A) == N):
        print('YES')
        print(' '.join(map(str, A)))
    else:
        print('NO')
    continue