Problem Statement

There is a simple connected undirected graph $G$ with $N$ vertices and $M$ edges, where the vertices are labeled $1,2,\dots,N$. The $i$-th edge connects two vertices $u_i$ and $v_i$.

Determine whether there exists a length-$N$ sequence of non-negative integers $X=(X_1,X_2,\dots,X_N)$ that satisfies all of the following conditions:

• $X_v$ does not exceed the degree of vertex $v$ in $G$ for each $v=1,2,\dots,N$.
• There is no directed graph obtained by assigning directions to the $M$ edges of $G$ in which, for each $v=1,2,\dots,N$, either the in-degree or the out-degree of $v$ equals $X_v$.

You have $T$ test cases; solve each of them.

Constraints

• $1 \leq T \leq 10^5$
• $2 \leq N \leq 2 \times 10^5$
• $N-1 \leq M \leq 2 \times 10^5$
• $1 \leq u_i, v_i \leq N$
• All input values are integers.
• The graph $G$ given in the input is a simple connected undirected graph.
• The sum of $N$ over all test cases in each input is at most $2 \times 10^5$.
• The sum of $M$ over all test cases in each input is at most $2 \times 10^5$.

Input

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

T
\mathrm{case}_1
\vdots
\mathrm{case}_T

Each case is given in the following format:

N M
u_1 v_1
u_2 v_2
\vdots
u_M v_M

Output

Print $T$ lines. The $i$-th line should contain the answer for the $i$-th test case. If there exists an $X$ that satisfies the conditions, print Yes; otherwise, print No.