103205: [Atcoder]ABC320 F - Fuel Round Trip

Problem Statement

You are planning to travel from coordinate $0$ to coordinate $X_N$ on a number line, then turn around and return to coordinate $0$. Here, you can only move in the positive direction on the outbound trip and in the negative direction on the return trip.
You will travel by car. The car consumes one liter of fuel for every unit distance it travels. You can carry up to $H$ liters of fuel and cannot move without fuel.
For each $i = 1, 2, \ldots, N-1$, there is a gas station at coordinate $X_i$, where you can get $F_i$ liters of fuel for $P_i$ yen. However, you cannot carry more than $H$ liters of fuel. More precisely, if you have $x$ liters of fuel and use the gas station at coordinate $X_i$, you must pay $P_i$ yen, and your amount of fuel becomes $\min(x + F_i, H)$ liters. Each gas station can be used at most once in total during the round trip.
Determine if you can achieve this plan when you initially have $H$ liters of fuel, and if it is possible, find the minimum amount of money required.

Constraints

• $1 \leq N, H \leq 300$
• $0 < X_1 < X_2 < \ldots < X_N \leq 10^5$
• $1 \leq P_i \leq 10^5$
• $1 \leq F_i \leq H$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

$N$ $H$
$X_1$ $X_2$ $\ldots$ $X_N$
$P_1$ $F_1$
$P_2$ $F_2$
$\vdots$
$P_{N-1}$ $F_{N-1}$

Output

If the plan can be achieved, print the minimum amount of money required; otherwise, print -1.

Sample Input 1

4 10
2 5 9 11
8 10
5 8
4 9

Sample Output 1

9

You can achieve the plan by using the gas station at coordinate $5$ on the outbound trip and the one at coordinate $9$ on the return trip, paying a total of $9$ yen.
It is impossible to achieve the plan by paying $8$ yen or less. Note that you cannot use the same gas station on both the outbound and return trips.

Sample Input 2

1 1
100000

Sample Output 2

-1

Sample Input 3

5 20
4 13 16 18 23
1 16
2 8
4 11
8 13

Sample Output 3

13