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 collections import defaultdict as dc
from collections import Counter 
from heapq import *
import math
from bisect import bisect_left,bisect
#bisect gives x and p[x] is element greater than it and out of bound for last one 
#p[x-1] gives equal or smaller and no error for any element.
import sys
from collections import deque as dq
from heapq import heapify,heappush,heappop
mod=10**9 +7
def sinp():
    p=str(input())
    return p
def inp(): 
    p=int(input())
    return p
def line():
    p=list(map(int,input().split()))
    return p
def read_mat():
    n=inp()
    a=[]
    for i in range(n):
        a.append(line())
    return a
def digit(n):
    s=str(n)
    p=0
    for i in s:
        p+=(int(i))**2
    return p
def check(p,i,j):
    z=i+(j-i)//2
    if p[z]-p[i] == p[j]-p[z]:
        #print(p[z]-p[i],p[j]-p[z])
        return j-i
    return 0
def solve(n,k):
    ans=[]
    s=0
    v=0
    if n%2==k%2:
        for i in range(k-1):
            ans.append(1)
        s=k-1
        if n-s<=0 or (n-s)%2==0:
            return "NO",[]
        ans.append(n-s)
        return "YES",ans
    else:
        for i in range(k-1):
            ans.append(2)
        s=2*(k-1)
        #print(n,s)
        if n-s<=0 or (n-s)%2!=0:
            return "NO",[]
        ans.append(n-s)
        return "YES",ans

for test in range(inp()):
    n,k=line()
    l,r=solve(n,k)
    print(l)
    if l=="YES":
        print(*r)