Interesting Array

题面翻译

构建一个序列 $a$，满足 $m$ 条限制。

限制形如 $l,r,q$：$a _ l\ \&\ a _ {l+1}\ \& \cdots \&\ a _ {r-1}\ \&\ a _ r = q$；(此处 $\&$ 为位运算的 AND 操作).

$1\le n,m\le 10^5,0\le q_i\le 2^{30}$

由 @Styx 提供翻译

题目描述

We'll call an array of $n$ non-negative integers a\[1\],a\[2\],...,a\[n\] interesting, if it meets $m$ constraints. The $i$ -th of the $m$ constraints consists of three integers $l_{i}$ , $r_{i}$ , $q_{i}$ ( $1<=l_{i}<=r_{i}<=n$ ) meaning that value should be equal to $q_{i}$ .

Your task is to find any interesting array of $n$ elements or state that such array doesn't exist.

Expression x&y means the bitwise AND of numbers $x$ and $y$ . In programming languages C++, Java and Python this operation is represented as "&", in Pascal — as "and".

输入格式

We'll call an array of $n$ non-negative integers a\[1\],a\[2\],...,a\[n\] interesting, if it meets $m$ constraints. The $i$ -th of the $m$ constraints consists of three integers $l_{i}$ , $r_{i}$ , $q_{i}$ ( $1<=l_{i}<=r_{i}<=n$ ) meaning that value should be equal to $q_{i}$ .

Your task is to find any interesting array of $n$ elements or state that such array doesn't exist.

Expression x&y means the bitwise AND of numbers $x$ and $y$ . In programming languages C++, Java and Python this operation is represented as "&", in Pascal — as "and".

输出格式

We'll call an array of $n$ non-negative integers a\[1\],a\[2\],...,a\[n\] interesting, if it meets $m$ constraints. The $i$ -th of the $m$ constraints consists of three integers $l_{i}$ , $r_{i}$ , $q_{i}$ ( $1<=l_{i}<=r_{i}<=n$ ) meaning that value should be equal to $q_{i}$ .

Your task is to find any interesting array of $n$ elements or state that such array doesn't exist.

Expression x&y means the bitwise AND of numbers $x$ and $y$ . In programming languages C++, Java and Python this operation is represented as "&", in Pascal — as "and".

样例 #1

样例输入 #1

3 1
1 3 3

样例输出 #1

YES
3 3 3

样例 #2

样例输入 #2

3 2
1 3 3
1 3 2

样例输出 #2

NO