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:
import sys
input=sys.stdin.readline
T=int(input())

for _ in range(0,T):
    N, K = list(map(int,input().split(" ")))

    onesum = 1 * (K - 1)
    twosum = 2 * (K - 1)
    oneremain = N - onesum
    tworemain = N - twosum
    if(oneremain < 0 and tworemain < 0):
        print("NO")
        continue
    # remain 1 is also hole
    if (tworemain % 2 == 0 and tworemain > 0):
        print("YES")
        outstring = ""
        for i in range(0,(K - 1)):
            outstring += "2 "
        if(tworemain == 0):
            print(outstring.strip())
        else:
            outstring += str(tworemain)
            print(outstring)
        continue
    elif (oneremain % 2 == 1 and oneremain > 0):
        print("YES")
        outstring = ""
        for i in range(0,(K - 1)):
            outstring += "1 "
        outstring += str(oneremain)
        print(outstring)
        continue

    else:
        print("NO")