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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

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