Same Parity Summands
Description
You are given two positive integers $n$ ($1 \le n \le 10^9$) and $k$ ($1 \le k \le 100$). 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 $a_1, a_2, \ldots, a_k$ such that all $a_i>0$, $n = a_1 + a_2 + \ldots + a_k$ 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.
The first line contains an integer $t$ ($1 \le t \le 1000$) — the number of test cases in the input. Next, $t$ test cases are given, one per line.
Each test case is two positive integers $n$ ($1 \le n \le 10^9$) and $k$ ($1 \le k \le 100$).
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.
Input
The first line contains an integer $t$ ($1 \le t \le 1000$) — the number of test cases in the input. Next, $t$ test cases are given, one per line.
Each test case is two positive integers $n$ ($1 \le n \le 10^9$) and $k$ ($1 \le k \le 100$).
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.
Samples
8
10 3
100 4
8 7
97 2
8 8
3 10
5 3
1000000000 9
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