CF1352B Same Parity Summands

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.