Given integers $c_{0}, c_{1}, \ldots, c_{k-1}$ we can define the cost of a number $0 \le x < 2^{k}$ as $p(x) = \sum_{i=0}^{k-1} \left( \left\lfloor \frac{x}{2^{i}} \right\rfloor \bmod 2 \right) \cdot c_{i}$. In other words, the cost of number $x$ is the sum of $c_{i}$ over the bits of $x$ which are equal to one.

Let's define the cost of array $a$ of length $n \ge 2$ with elements from $[0, 2^{k})$ as follows: $cost(a) = \sum_{i=1}^{n - 1} p(a_{i} \oplus a_{i+1})$, where $\oplus$ denotes bitwise exclusive OR operation.

You have to construct an array of length $n$ with minimal cost, given that each element should belong to the given segment: $l_{i} \le a_{i} \le r_{i}$.

The first line contains two integers $n$ and $k$ ($2 \le n \le 50$, $1 \le k \le 50$) — the size of an array and bit length of the numbers in question.

Next $n$ lines contain the restrictions for elements of the array: the $i$-th line contains two integers $l_{i}$ and $r_{i}$ ($0 \le l_{i} \le r_{i} < 2^{k}$).

The last line contains integers $c_{0}, c_{1}, \ldots, c_{k-1}$ ($0 \le c_{i} \le 10^{12}$).

Output one integer — the minimal cost of an array satisfying all the restrictions.