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
import heapq
import cProfile, math
from collections import Counter, defaultdict, deque
from bisect import bisect_left, bisect, bisect_right
import itertools
from copy import deepcopy
from fractions import Fraction
import sys, threading
import operator as op
from functools import reduce
import sys


def get_int():
    return int(stdin.readline().strip())


def get_tuple():
    return map(int, stdin.readline().split())


def get_list():
    return list(map(int, stdin.readline().split()))


def solve():
    n,k = get_tuple()
    if n%2!=0 and k%2==0:
        print("NO")
    elif n%2==0 and k%2!=0:
        if n<2*k:
            print("NO")
        else:
            print("YES")
            ans = [2]*(k-1)
            ans.append(n-sum(ans))
            print(*ans)
    elif n%2!=0 and k%2!=0:
        if n<k:
            print("NO")
        elif n==k:
            print("YES")
            ans = [1]*k
            print(*ans)
        else:
            print("YES")
            ans = [1]*(k-1)
            ans.append(n-sum(ans))
            print(*ans)
    else:
        if n<k:
            print("NO")
        elif n == k:
            print("YES")
            ans = [1] * k
            print(*ans)
        elif k<n<2*k:
            ans = [1]*(k-1)
            ans.append(n-sum(ans))
            print("YES")
            print(*ans)
        else:
            print("YES")
            ans = [2] * (k - 1)
            ans.append(n - sum(ans))
            print(*ans)


def main():
    solve()

TestCases = True

if TestCases:
    for i in range(get_int()):
        main()
else:
    main()