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:
# cook your dish here
MOD =  1000000007
#import time
#import heapq
#import math
#import string
#import bisect


def solve(n,k):
    ans = []
    k1 = k
    if n>=k:
        while k1!=1:
            ans.append(1)
            k1-=1
        val2 = n-sum(ans)
        if val2>0 and val2%2==1:
            ans.append(val2)
            print("YES")
            print(*ans,sep=" ")
        else:
            #print("second")
            ans.clear()
            k1 = k
            while k1!=1:
                ans.append(2)
                k1-=1
            val2 = n-sum(ans)
            if val2>0 and val2%2==0:
                ans.append(val2)
                print("YES")
                print(*ans,sep=" ")
            else:
                #print("thired")
                print("NO")
    else:
        print("NO")
     
            
for i in range(int(input())):
    #x,y,l,r= map(int,input().split())
    n,k= map(int,input().split())
    #n = int(input())
    #a = list(map(int,input().split()))
    #b = list(map(int,input().split()))
    #l,r= map(int,input().split())
    #n = int(input())
    #s = input()
    #sa = list(map(str,input().split()))
    #b = list(map(int,input().split()))
    #st = time.process_time()
    solve(n,k)
    #print(s)
    #pt = solve(s)
    #print(pt)
    #print("yes" if pt==1 else "no")
    #print("Linear : ",time.process_time() - st)