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 math

t = int(input())

for i in range(t):
    n,k = map(int, input().split())

    ans = []
    flag = True 

    if(k > n):
        flag = False 

    else:
        quotient =  n//k
        remainder = n % k

        if(remainder % 2 == 0):
            ans = [quotient] * k
            ans[0] += remainder
            flag = True

        else:
            if(k % 2 == 1):
                part1 = [quotient + remainder, quotient + k-2]
                part2 = [quotient - 1] * (k-2)
                part1.extend(part2)
                ans.extend(part1)
                if(quotient-1 <= 0):
                    flag = False

                else:
                    flag = True

            else:
                flag = False


    if(flag):
        print("YES")
        print(* ans)
        
    else:
        print("NO")