No submission language available for this problem.

Description

Input

The first line contains 2 integers $n$ and $q$ $(2 \leq n \leq 3 \cdot 10^5; 1 \leq q \leq 3 \cdot 10^5)$ — the number of points and the number of queries.

Then, $n$ lines follows, the $i$-th of them contains two integers $x_i$ and $w_i$ $(-10^9 \leq x_i \leq 10^9; 1 \leq w_i \leq 10^9)$ — the coordinate and the weight of the $i$-th point.

It is guaranteed that the points are given in the increasing order of $x$.

Then, $q$ lines follows, the $i$-th of them contains two integers $l_i$ and $r_i$ $(1 \leq l_i < r_i \leq n)$ — the given subarray of the $i$-th query.

Output

For each query output one integer, the minimum weighted distance among all pair of distinct points in the given subarray.

Samples

5 5
-2 2
0 10
1 1
9 2
12 7
1 3
2 3
1 5
3 5
2 4

9
11
9
24
11

Note

For the first query, the minimum weighted distance is between points $1$ and $3$, which is equal to $|x_1 - x_3| \cdot (w_1 + w_3) = |-2 - 1| \cdot (2 + 1) = 9$.

For the second query, the minimum weighted distance is between points $2$ and $3$, which is equal to $|x_2 - x_3| \cdot (w_2 + w_3) = |0 - 1| \cdot (10 + 1) = 11$.

For the fourth query, the minimum weighted distance is between points $3$ and $4$, which is equal to $|x_3 - x_4| \cdot (w_3 + w_4) = |1 - 9| \cdot (1 + 2) = 24$.