Score : $1700$ points
There is a railroad in Takahashi Kingdom. The railroad consists of $N$ sections, numbered $1$, $2$, ..., $N$, and $N+1$ stations, numbered $0$, $1$, ..., $N$. Section $i$ directly connects the stations $i-1$ and $i$. A train takes exactly $A_i$ minutes to run through section $i$, regardless of direction. Each of the $N$ sections is either single-tracked over the whole length, or double-tracked over the whole length. If $B_i = 1$, section $i$ is single-tracked; if $B_i = 2$, section $i$ is double-tracked. Two trains running in opposite directions can cross each other on a double-tracked section, but not on a single-tracked section. Trains can also cross each other at a station.
Snuke is creating the timetable for this railroad. In this timetable, the trains on the railroad run every $K$ minutes, as shown in the following figure. Here, bold lines represent the positions of trains running on the railroad. (See Sample 1 for clarification.)
When creating such a timetable, find the minimum sum of the amount of time required for a train to depart station $0$ and reach station $N$, and the amount of time required for a train to depart station $N$ and reach station $0$. It can be proved that, if there exists a timetable satisfying the conditions in this problem, this minimum sum is always an integer.
Formally, the times at which trains arrive and depart must satisfy the following:
The input is given from Standard Input in the following format:
$N$ $K$ $A_1$ $B_1$ $A_2$ $B_2$ : $A_N$ $B_N$
Print an integer representing the minimum sum of the amount of time required for a train to depart station $0$ and reach station $N$, and the amount of time required for a train to depart station $N$ and reach station $0$. If it is impossible to create a timetable satisfying the conditions, print $-1$ instead.
3 10 4 1 3 1 4 1
26
For example, the sum of the amount of time in question will be $26$ minutes in the following timetable:
In this timetable, the train represented by the red line departs station $0$ at time $0$, arrives at station $1$ at time $4$, departs station $1$ at time $5$, arrives at station $2$ at time $8$, and so on.
1 10 10 1
-1
6 4 1 1 1 1 1 1 1 1 1 1 1 1
12
20 987654321 129662684 2 162021979 1 458437539 1 319670097 2 202863355 1 112218745 1 348732033 1 323036578 1 382398703 1 55854389 1 283445191 1 151300613 1 693338042 2 191178308 2 386707193 1 204580036 1 335134457 1 122253639 1 824646518 2 902554792 2
14829091348