Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

F. Mice and Holes

time limit per test

1.5 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputOne day Masha came home and noticed *n* mice in the corridor of her flat. Of course, she shouted loudly, so scared mice started to run to the holes in the corridor.

The corridor can be represeted as a numeric axis with *n* mice and *m* holes on it. *i*th mouse is at the coordinate *x*_{i}, and *j*th hole — at coordinate *p*_{j}. *j*th hole has enough room for *c*_{j} mice, so not more than *c*_{j} mice can enter this hole.

What is the minimum sum of distances that mice have to go through so that they all can hide in the holes? If *i*th mouse goes to the hole *j*, then its distance is |*x*_{i} - *p*_{j}|.

Print the minimum sum of distances.

Input

The first line contains two integer numbers *n*, *m* (1 ≤ *n*, *m* ≤ 5000) — the number of mice and the number of holes, respectively.

The second line contains *n* integers *x*_{1}, *x*_{2}, ..., *x*_{n} ( - 10^{9} ≤ *x*_{i} ≤ 10^{9}), where *x*_{i} is the coordinate of *i*th mouse.

Next *m* lines contain pairs of integer numbers *p*_{j}, *c*_{j} ( - 10^{9} ≤ *p*_{j} ≤ 10^{9}, 1 ≤ *c*_{j} ≤ 5000), where *p*_{j} is the coordinate of *j*th hole, and *c*_{j} is the maximum number of mice that can hide in the hole *j*.

Output

Print one integer number — the minimum sum of distances. If there is no solution, print -1 instead.

Examples

Input

4 5

6 2 8 9

3 6

2 1

3 6

4 7

4 7

Output

11

Input

7 2

10 20 30 40 50 45 35

-1000000000 10

1000000000 1

Output

7000000130

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jul/21/2017 01:42:23 (c2).

Desktop version, switch to mobile version.

User lists

Name |
---|