We have a directed graph with $N$ vertices and $M$ edges. The vertices are numbered from $1$ through $N$, and the $i$-th edge goes from vertex $U_i$ to vertex $V_i$.

You are currently at vertex $1$. Determine if you can make the following move $10^{10^{100}}$ times to end up at vertex $1$:

-   choose an edge going from the vertex you are currently at, and move to the vertex that the edge points at.

Given $T$ test cases, solve each of them.

The input is given from Standard Input in the following format. Here, $\text{test}_i$ denotes the $i$-th test case.

```
$T$
$\text{test}_1$
$\text{test}_2$
$\vdots$
$\text{test}_T$
```

Each test case is given in the following format.

```
$N$ $M$
$U_1$ $V_1$
$U_2$ $V_2$
$\vdots$
$U_M$ $V_M$
```

Print $T$ lines.

The $i$-th $(1\leq i \leq T)$ line should contain `Yes` if you can make the move described in the problem statement $10^{10^{100}}$ times to end up at vertex $1$, and `No` otherwise.

-   All input values are integers.
-   $1\leq T \leq 2\times 10^5$
-   $2\leq N \leq 2\times 10^5$
-   $1\leq M \leq 2\times 10^5$
-   The sum of $N$ over all test cases is at most $2 \times 10^5$.
-   The sum of $M$ over all test cases is at most $2 \times 10^5$.
-   $1 \leq U_i, V_i \leq N$
-   $U_i \neq V_i$
-   If $i\neq j$, then $(U_i,V_i) \neq (U_j,V_j)$.

Yes
No
No
Yes

For the 1-st test case,

• You inevitably repeat visiting vertices 1→2→1→…. Thus, you will end up at vertex 1 after making the move $10^{{10}^{100}}$ times, so the answer is Yes.

For the 2-nd test case,

• You inevitably repeat visiting vertices 1→2→3→1→…. Thus, you will end up at vertex 2 after making the move $10^{{10}^{100}} times, so the answer is No.