write a go solution for Description:
There are n weighted points on the OX-axis. The coordinate and the weight of the i-th point is x_i and w_i, respectively. All points have distinct coordinates and positive weights. Also, x_i<x_i+1 holds for any 1<=i<n.

The weighted distance between i-th point and j-th point is defined as |x_i-x_j|*(w_i+w_j), where |val| denotes the absolute value of val.

You should answer q queries, where the i-th query asks the following: Find the minimum weighted distance among all pairs of distinct points among the points in subarray [l_i,r_i].

Input Format:
The first line contains 2 integers n and q (2<=qn<=q3*10^5;1<=qq<=q3*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<=x_i<=10^9;1<=w_i<=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<=l_i<r_i<=n) — the given subarray of the i-th query.

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

Note:
For the first query, the minimum weighted distance is between points 1 and 3, which is equal to |x_1-x_3|*(w_1+w_3)=|-2-1|*(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|*(w_2+w_3)=|0-1|*(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|*(w_3+w_4)=|1-9|*(1+2)=24.. Output only the code with no comments, explanation, or additional text.