时间限制:C/C++/Rust/Pascal 1秒,其他语言2秒
空间限制:C/C++/Rust/Pascal 1024 M,其他语言2048 M
Special Judge, 64bit IO Format: %lld

题目描述

Construct a string S of length n with the character set \{0, 1, 2\} such that there are exactly k square substrings.

A square substring is a string of the form TT, where T is any non-empty substring. For example, the string aaa has two square substrings.

输入描述:

The first line of input contains two integers n and k.

输出描述:

If there is a solution, output Yes on the first line. On the second line, output n integers representing each character of the string S.

Otherwise, output No on a single line.
示例1

输入

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6 2

输出

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Yes
0 2 0 0 2 0
示例2

输入

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8 5

输出

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Yes
0 0 1 1 0 0 1 1
示例3

输入

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6 13

输出

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No

备注:

0 \leq n, k \leq 10^5.