After being invaded by the Kingdom of AlDebaran, bombs are planted throughout our country, AtCoder Kingdom.

Fortunately, our military team called ABC has managed to obtain a device that is a part of the system controlling the bombs.

There are $N$ bombs, numbered $1$ to $N$, planted in our country. Bomb $i$ is planted at the coordinate $A_i$. It is currently activated if $B_i=1$, and deactivated if $B_i=0$.

The device has $M$ cords numbered $1$ to $M$. If we cut Cord $j$, the states of all the bombs planted between the coordinates $L_j$ and $R_j$ (inclusive) will be switched - from activated to deactivated, and vice versa.

Determine whether it is possible to deactivate all the bombs at the same time. If the answer is yes, output a set of cords that should be cut.

Input is given from Standard Input in the following format:

```
$N$ $M$
$A_1$ $B_1$
$:$
$A_N$ $B_N$
$L_1$ $R_1$
$:$
$L_M$ $R_M$
```

If it is impossible to deactivate all the bombs at the same time, print -1. If it is possible to do so, print a set of cords that should be cut, as follows:

$k$ 

$c_1$ $c_2$ $\dots$ $c_k$

Here, $k$ is the number of cords (possibly $0$), and $c_1, c_2, \dots, c_k$ represent the cords that should be cut. $1 \leq c_1 < c_2 < \dots < c_k \leq M$ must hold.

-   All values in input are integers.
-   $1 \leq N \leq 10^5$
-   $1 \leq A_i \leq 10^9\ (1 \leq i \leq N)$
-   $A_i$ are pairwise distinct.
-   $B_i$ is $0$ or $1$. $(1 \leq i \leq N)$
-   $1 \leq M \leq 2 \times 10^5$
-   $1 \leq L_j \leq R_j \leq 10^9\ (1 \leq j \leq M)$

2
1 4

There are two activated bombs at the coordinates $5, 10$, and one deactivated bomb at the coordinate $8$.

Cutting Cord $1$ switches the states of all the bombs planted between the coordinates $1$ and $10$, that is, all of the three bombs.

Cutting Cord $4$ switches the states of all the bombs planted between the coordinates $8$ and $9$, that is, Bomb $3$.

Thus, we can deactivate all the bombs by cutting Cord $1$ and Cord $4$.

-1

Cutting any set of cords will not deactivate all the bombs at the same time.

0

All the bombs are already deactivated, so we do not need to cut any cord.

5
1 7 8 9 11

If there are multiple sets of cords that deactivate all the bombs when cut, any of them can be printed.