Problem G
Generators

The volcanic island of Fleeland has never had a proper electric net, but finally the administration of the island have agreed to build the island’s power plants and network.

On the island’s coast are its $n$ cities. The administration has surveyed the cities and proposed $m$ of them as possible locations for a power plant, with the $i$th proposal stating that the company can build a plant in city $c_ i$ for cost $a_ i$.

These power plants are very modern and a single plant could power the whole island, but the volcano makes building power lines across the island a dangerous affair. For $1 \leq i < n$, the company can build power lines between cities $i$ and $i+1$ for a cost of $b_ i$, and between cities $n$ and $1$ for a cost of $b_ n$. A city will receive power if it contains a power plant or is connected to a city with a power plant via power lines.

What is the cheapest way to power all the cities on the island?

Input

• One line containing two integers $n$ ($3\leq n \leq 10^5$) and $m$ ($1\leq m \leq n$), the number of cities and the number of possible locations for a power plant.

• Then follow $m$ lines, the $i$th of which contains $c_ i$ ($1 \leq c_ i \leq n$) and $a_ i$ ($1 \leq a_ i \leq 10^9$), the $i$th possible location for a power plant, and the cost to build it.

• Then follows a line containing $n$ integers $b_ i$ ($1 \leq b_ i \leq 10^9$), the costs of building the power lines.

The values of $c_{1,\ldots ,n}$ are unique and given in strictly increasing order.

Output

Output the minimal cost of powering all cities on the island.

3 2
1 100
2 200
150 300 150

400

3 2
1 100
2 200
300 300 150

450