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:
import sys, heapq
from collections import *
from functools import lru_cache
sys.setrecursionlimit(10**6)



def main():

    # sys.stdin = open('input.txt', 'r')
    t = int(input())
    for _ in range(t):
        n, k = map(int, input().split(' '))
        # n = int(input())
        nn, kk = n&1, k&1
        flag, res = False, []
        if nn ^ kk == 0:
            if n >= k:
                flag = True
                res = [n-k+1]+[1]*(k-1)
        elif nn == 0 and kk == 1:
            if n >= k*2:
                flag = True
                res = [n-k*2+2]+[2]*(k-1)
        if len(res) > 0:
            print("YES")
            print(' '.join(map(str,res)))
        else:
            print("NO")


if __name__ == "__main__":
    main()