Problem Statement

An undirected graph with numbered vertices is called a good graph if it has a spanning tree $T$ that satisfies the following condition. Here, an edge connecting two vertices $u$ and $v$ $(u < v)$ is denoted as edge $(u,v)$.

• For every edge $(u,v)$ $(u < v)$ in the graph, the minimum and maximum vertex numbers on the unique simple path connecting vertices $u$ and $v$ in $T$ are $u$ and $v$, respectively.

You are given a simple connected undirected graph $G$ with $N$ vertices numbered from $1$ to $N$. The graph $G$ has $M$ edges, and the $i$-th edge connects vertices $A_i$ and $B_i$ $(A_i < B_i)$.

For each $i=1,2,\dots,M$, determine whether the graph obtained by removing the $i$-th edge from $G$ is a good graph.

Constraints

• $2 \leq N \leq 2 \times 10^5$
• $N-1 \leq M \leq 2 \times 10^5$
• $1 \leq A_i < B_i \leq N$
• All input values are integers.
• The given graph is a simple connected undirected graph.

Input

The input is given from Standard Input in the following format:

N M
A_1 B_1
\vdots
A_M B_M

Output

Print $M$ lines. The $i$-th line should contain Yes if the graph obtained by removing the $i$-th edge from $G$ is a good graph, and No otherwise.