Given a directed graph of $N$ vertices and $M$ edges, determine for each edge if it is possible to reach vertex $N$ from vertex $1$ given that that edge is deleted from the graph.

Constraints

$1\le N\le 50$

$1\le M\le N^2-N$

$1\le s_i,t_i\le N,s_i\ne t_i$

Input Specification

The first line of the input contains two space-separated integers, $N$ and $M$.

Each of the next $M$ lines contains two space-separated integers, $s_i$ and $t_i$, indicating that the $i$th edge goes from vertex $s_i$ to $t_i$.

You may assume that any given tuple $(s_i,t_i)$ appears at most once.

Output Specification

Output $M$ lines.

On the $i$th line, given that the $i$th edge is deleted, print YES if it is still possible to reach vertex $N$ from vertex $1$. Print NO otherwise.

Sample Input

3 3
1 2
2 1
2 3

Sample Output

NO
YES
NO