Same Parity Summands

You are given two positive integers n (1 ≤ n ≤ 10^9) and k (1 ≤ k ≤ 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, …, a_k such that all a_i>0, n = a_1 + a_2 + … + 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 ≤ t ≤ 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 ≤ n ≤ 10^9) and k (1 ≤ k ≤ 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

inputFormat

Input

The first line contains an integer t (1 ≤ t ≤ 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 ≤ n ≤ 10^9) and k (1 ≤ k ≤ 100).

outputFormat

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

样例

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

yes
2 2 6
yes
1 1 1 97
no
no
yes
1 1 1 1 1 1 1 1
no
yes
1 1 3
yes
2 2 2 2 2 2 2 2 999999984

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