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:
#!/bin/python3

import math
import os
import random
import re
import sys

def printarr(arr):
    for z in arr:
        if type(z) is list:
            for k in z:
                print(k,end=" ")
        else:
            print(z,end=" ")
    print(end="\n")

def solve(n,k):
    if n<k:
        print("NO")
    else:
        div=int(n/k)
        rem=n%k
        if((rem+div)%2==1 and div%2==1):
            print("YES");
            for i in range(k-1):
                print(div,end=" ")
            print(div+rem)
        elif((rem+div)%2==0 and div%2==0):
            print("YES");
            for i in range(k-1):
                print(div,end=" ")
            print(div+rem)
        else:
            if((k-1)%2!=0 or div==1):
                print("NO")
            else:
                print("YES")
                for i in range(int(k/2)):
                    print(div+1,div-1,end=" ")
                print(div+rem)


if __name__ == '__main__':
    t=int(input())
    while t>0:
        ins=list(input().split())
        n=int(ins[0])
        k=int(ins[1])
        t-=1
        solve(n,k)