B. Same Parity Summandstime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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.InputThe 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).OutputFor 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.ExampleInput
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

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 
['constructive algorithms', 'math', '*1200']