Interesting Array

Source: Codeforces

Version: Phuoc Hung OJ Extended

Problem Statement

Construct a non-negative integer array whose bitwise AND on every constrained range equals the required value, or report impossibility.

Input

The first line contains $n,m$. Each of the next $m$ lines contains $l_i,r_i,q_i$, requiring $a_{l_i}\mathbin{\&}a_{l_i+1}\mathbin{\&}\cdots\mathbin{\&}a_{r_i}=q_i$.

Output

Print NO if no array exists. Otherwise print YES and then $n$ values satisfying every constraint. Multiple answers are allowed and are checked by a special checker.

Subtasks

• 20 points: $n,m\le50$.
• 30 points: $n,m\le5000$.
• 50 points: $n,m\le10^5$, $0\le q_i<2^{30}$, $0\le a_i<2^{30}$.

Examples

Input

3 1
1 3 3

Output

YES
3 3 3

Explanation

The only constraint requires the AND of all three positions to be 3. Array 3 3 3 is valid because $3\mathbin{\&}3\mathbin{\&}3=3$. Other valid arrays may also exist.