Machine Gun

Fulanito went to play an old arcade game. In the game, he can place a machine gun anywhere in his base, which consists of all points $(x, y)$ with integer coordinates and $x < 0$. There are $N$ enemies on the battlefield. The $i$-th enemy ($1 \le i \le N$) is at position $(x_i, y_i)$ with $x_i > 0$. All positions are given in advance.

A machine gun placed at $(x_m, y_m)$ covers a viewing angle facing right, centered on the line $y = y_m$, whose boundaries are given by the lines $y = y_m \pm (x - x_m)/2$. Once placed, it hits every enemy in the region bounded by this angle, including those located on the boundary lines.

Figure 1: Pictorial representation of the sample input

The scoring system used by this game is unnecessarily complicated; many believe that such a system was a big mistake by the developers (who, in response, state with conviction that “it's not a bug, it's a feature!”). Specifically, the score obtained by a given placement of the machine gun is computed by performing the following steps:

• List the indices ($i$ between 1 and $N$) of all enemies the machine gun hits.
• Sort the indices in increasing order, and call the sorted values $i_0 < i_1 < \cdots < i_{k-1}$.
• Compute the score using the formula $(\sum_{j=0}^{k-1} i_j \cdot 5782344^j) \bmod (10^9 + 7)$, where $a \bmod b$ denotes the remainder of dividing $a$ by $b$.
• Note: A machine gun that hits no enemies receives a score exactly equal to 0.

To get better at this game, Fulanito asks you $Q$ questions: each query asks for the score that would be obtained if we placed the machine gun at a certain position $(x_m, y_m)$. To make the problem more challenging, the values of $(x_m, y_m)$ are not given directly. Instead, values $a$ and $b$ are given, which can be used to compute $x_m$ and $y_m$ through the formulas $x_m = -1 - (p + a) \bmod (10^9 + 7)$ and $y_m = (p + b) \bmod (10^9 + 7)$, where $p$ is the answer to the previous query ($p = 0$ when processing the first query).

NOTE: It is guaranteed that the sum of the number of enemies hit across all queries is at most $10^6$.

The input consists of several lines. The first line of the input contains two integers $N, Q$ ($1 \le N, Q \le 10^5$), the number of enemies and the number of queries.

The next $N$ lines of the input contain two integers each: $x_i$ and $y_i$ ($1 \le x_i, y_i \le 10^9$), the coordinates of the position of the $i$-th enemy.

The next $Q$ lines contain two integers each: the values $a$ and $b$ ($0 \le a, b < 10^9 + 7$) that specify each query, as explained in the statement.

For each query, print a single integer containing the answer to the query.