Same Parity Summands

1000ms

262144K

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.

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.

Sample Input:

8
10 3
100 4
8 7
97 2
8 8
3 10
5 3
1000000000 9

Sample 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

Informação

Provedor Codeforces

Código CF1352B