Train Travel

There are $N$ cities on a line numbered $1$ to $N$. Rail $i$ connects cities $i$ and $i+1$ bidirectionally.

For each rail you may pay ticket fare $A_i$ per ride, or buy a rail-specific IC card for $C_i$ once and pay $B_i$ per ride on that rail ($A_i > B_i$). You start with no cards.

You visit cities $P_1, P_2, \ldots, P_M$ in order, moving from $P_j$ to $P_{j+1}$ on day $j$. Minimize total spending on card purchases plus rides.

Line 1: $N$, $M$. Line 2: $P_1, \ldots, P_M$. Next $N-1$ lines: $A_i$, $B_i$, $C_i$ for rail $i$.

Print the minimum total cost.

$2 \leq N, M \leq 100000$, $1 \leq B_i < A_i \leq 100000$, $1 \leq C_i \leq 100000$, $1 \leq P_j \leq N$, and $P_j \neq P_{j+1}$.