Card Collection

JOI-kun is enthusiastic about collecting cards in a card game. Each card in the card game has two integers representing its strength and cost. To obtain a new card, JOI-kun brings $N$ cards to a card exchange. Each card is numbered from $1$ to $N$. The strength of card $i$ ($1 ≤ i ≤ N$) is $S_i$ and the cost of card $i$ is $V_i$.

There are two machines available in the card exchange. If you insert two cards, A and B, into one of the machines, you will be able to receive any card C satisfying the following conditions.

• If you use the first machine, then the strength of C must be equal to the maximum of the strength of A and B, and the cost of C must be equal to the maximum of the cost of A and B.
• If you use the second machine, then the strength of C must be equal to the minimum of the strength of A and B, and the cost of C must be equal to the minimum of the cost of A and B.

JOI-kun plans to use the machines exactly $N - 1$ times to obtain a new card. To do this, he lines up the $N$ cards in a row from card $1$ to card $N$. He then repeats the following operation $N - 1$ times.

Choose two adjacent cards, exchange them with a new card using one of the machines, and place the new card where the chosen two cards were in the row before the operation.

After performing $N-1$ operations, JOI-kun will have only one card left. The strength and cost of this card will depend on the operations he performs. JOI-kun has a list of $M$ cards that he wants to obtain after performing $N - 1$ operations. The $j$-th card ($1 ≤ j ≤ M$) is represented by a pair of integers $(T_j , W_j)$, where $T_j$ is the strength and $W_j$ is the cost of the $j$-th card. Write a program that, given information about JOI-kun’s cards and the list of cards he wants to obtain, determines all the cards in the list that he can obtain after performing $N - 1$ operations.

Read the following data from the standard input.

$N$ $M$

$S_1$ $V_1$

$S_2$ $V_2$

$\vdots$

$S_N$ $V_N$

$T_1$ $W_1$

$T_2$ $W_2$

$\vdots$

$T_M$ $W_M$

Write one line to the standard output. The output should contain the indices of all the cards in the list that JOI-kun can obtain after performing $N - 1$ operations in increasing order.

• $2 ≤ N ≤ 200\, 000$.
• $1 ≤ M ≤ 200\, 000$.
• $1 ≤ S_i ≤ 10^9$ ($1 ≤ i ≤ N$).
• $1 ≤ V_i ≤ 10^9$ ($1 ≤ i ≤ N$).
• $1 ≤ T_j ≤ 10^9$ ($1 ≤ j ≤ M$).
• $1 ≤ W_j ≤ 10^9$ ($1 ≤ j ≤ M$).
• Given values are all integers.