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:
from sys import stdin,stdout
from itertools import combinations
from collections import defaultdict,Counter
import math
 
def listIn():
    return list((map(int,stdin.readline().strip().split())))
 
def stringListIn():
    return([x for x in stdin.readline().split()])
    
def intIn():
    return (int(stdin.readline()))
 
def stringIn():
    return (stdin.readline().strip())
    
    
 
if __name__=="__main__":
    t=int(input())
    while(t>0):
        t-=1
        n,k=listIn()
        if k>n:
            print('NO')
        else:
            if n%k==0:
                d=n//k
                li=[d]*k
                print("YES")
                print(*li)
            else:
                rem=n%k
                d=n//k
                if rem%2==0:
                    print('YES')
                    li=[d]*(k-1)+[d+rem]
                    print(*li)
                else:
                    if (rem+k)%2==0:
                        if d-1==0:
                            print('NO')
                        else:
                            li=[d-1]*(k-1)+[d+rem+k-1]
                            print('YES')
                            print(*li)
                    else:
                        print('NO')