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:
############ ---- Input Functions ---- ############
def readInt():
    return(int(input()))
def readList():
    return(list(map(int,input().rstrip().split())))
def readString():
    s = input()
    return s
def readInts():
    return(map(int,input().rstrip().split()))

def solve(n, k):
    rest = n - (k-1)
    if rest > 0 and rest % 2 == 1:
        print("YES")
        r = []
        for i in range(k-1):
            r.append(1)
        r.append(rest)
        print(" ".join([str(e) for e in r]))
        return

    rest_2 = n - (k-1)*2
    if rest_2 > 0 and rest_2 % 2 == 0:
        print("YES")
        r = []
        for i in range(k-1):
            r.append(2)
        r.append(rest_2)
        print(" ".join([str(e) for e in r]))
        return

    print("NO")


t = readInt()
for i in range(t):
    n, k = readInts()
    solve(n, k)