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B. Same Parity Summands

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard 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.

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.

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

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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