Interesting Array

1000ms

262144K

Description:

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 $\text{[math]}$ 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".

Input:

The first line contains two integers n, m (1 ≤ n ≤ 10⁵, 1 ≤ m ≤ 10⁵) — the number of elements in the array and the number of limits.

Each of the next m lines contains three integers l_i, r_i, q_i (1 ≤ l_i ≤ r_i ≤ n, 0 ≤ q_i < 2³⁰) describing the i-th limit.

Output:

If the interesting array exists, in the first line print "YES" (without the quotes) and in the second line print n integers a[1], a[2], ..., a[n] (0 ≤ a[i] < 2³⁰) decribing the interesting array. If there are multiple answers, print any of them.

If the interesting array doesn't exist, print "NO" (without the quotes) in the single line.

Sample Input:

3 1
1 3 3

Sample Output:

YES
3 3 3

Sample Input:

3 2
1 3 3
1 3 2

Sample Output:

NO

Informação

Provedor Codeforces

Código CF482B