Cetinska Road Construction

A river runs through a desert, with a city on each of its two ends. The river is a polyline that starts at one city and ends at the other.

Every straight segment of the river flows strictly from south to north, that is, in the direction of increasing $y$ coordinate.

We must build a road connecting the two cities. The road may run along the river, but it cannot simply cross it: a bridge must be built at every crossing. Building one meter of road on the ground costs $1$, and building each bridge (crossing) costs $T$.

Traffic inside the cities is already handled, so the road may start and end on either bank of the river.

The first line contains a natural number $N$ ($2 ≤ N ≤ 1500$), the number of river vertices (including the cities), and a real number $T$ ($0 < T ≤ 10^6$), the cost of one bridge. $T$ has at most two decimal places.

Each of the next $N$ lines contains two integers $X_i$ and $Y_i$, the coordinates of the $i$-th river vertex, with $|X_i|, |Y_i| ≤ 10^5$. They satisfy $Y_i < Y_{i+1}$ for $1 ≤ i < N$.

No three points in the input are collinear. The road must start at $(X_1, Y_1)$ and end at $(X_N, Y_N)$.

Print one number, the minimum possible cost of the project. The answer is accepted if it differs from the exact answer by at most $10^{-6}$.

See the figure for the explanation of the first sample.