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
'''
#include <iostream>
#include<bits/stdc++.h>
#include<math.h>
using namespace std;

int main() {
	int t;
	scanf("%d",&t);
	while(t--)
	{
	    long long int x,y,r,l,i;
	Tuppence Middleton - IMDbwww.imdb.com › name
Tuppence Middleton (born 21 February 1987) is an English actress. She was nominated for the ... 2019 A Working Mom's Nightmare (TV Movie) Hannah ... 2014 The Great War: The People's Story (TV Mini-Series documentary) Diana Manners.

Tuppence Middleton on IMDb: Movies, TV, Celebs, and more ...www.imdb.com › name › mediaindex
Tuppence Middleton photos, including production stills, premiere photos and other event photos, publicity photos, behind-the-scenes, and more.

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Jump to: Downton Abbey Lucy Smith 2019. Sense8 Riley 25 Episodes (2015-2016) The Current War: Director's Cut Mary Edison 2017. Jupiter Ascending Kalique Abrasax 2015. Masterpiece Iris 1 Episode (2013) Inspector Lewis on Masterpiece Vicki Walmsley 1 Episode (2013) Spies of Warsaw Gabrielle 8 Episodes (2013-2019)


void decToBinary(int n,vector<int>* v) 
{ 
    // array to store binary number 
    int binaryNum[50]; 
  
    // counter for binary array 
    int i = 0; 
    while (n > 0) { 
  
        // storing remainder in binary array 
        binaryNum[i] = n % 2;  



'''
#lannisters don't act like fools

import math
t=int(input())
for _ in range(0,t):
    str1=input()
    str1=str1.split()
    n=int(str1[0])
    k=int(str1[1])
    sum1=(k-1)
    sum2=(k-1)*2
    if (n-sum1)>0 and (n-sum1)%2==1:
        print("YES")
        for i in range(0,k-1):
            print(1,end=' ')
        print(n-sum1)
    elif (n-sum2)>0 and (n-sum2)%2==0:
        print("YES")
        for i in range(0,k-1):
            print(2,end=' ')
        print(n-sum2)
    else:
        print("NO")