Codeforces Round 772 (Div. 2) |
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Finished |

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data structures

greedy

*2800

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F. Closest Pair

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThere 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 $$$1 \leq i < n$$$.

The weighted distance between $$$i$$$-th point and $$$j$$$-th point is defined as $$$|x_i - x_j| \cdot (w_i + w_j)$$$, 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

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.

Example

Input

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

Output

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 $$$|x_3 - x_4| \cdot (w_3 + w_4) = |1 - 9| \cdot (1 + 2) = 24$$$.

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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