Codeforces Round #380 (Div. 2, Rated, Based on Technocup 2017 - Elimination Round 2)C. Road to Cinema 二分

C. Road to Cinema

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

Vasya is currently at a car rental service, and he wants to reach cinema. The film he has bought a ticket for starts in t minutes. There is a straight road of length s from the service to the cinema. Let's introduce a coordinate system so that the car rental service is at the point 0, and the cinema is at the point s.

There are k gas stations along the road, and at each of them you can fill a car with any amount of fuel for free! Consider that this operation doesn't take any time, i.e. is carried out instantly.

There are n cars in the rental service, i-th of them is characterized with two integers c_i and v_i — the price of this car rent and the capacity of its fuel tank in liters. It's not allowed to fuel a car with more fuel than its tank capacity v_i. All cars are completely fueled at the car rental service.

Each of the cars can be driven in one of two speed modes: normal or accelerated. In the normal mode a car covers 1 kilometer in 2 minutes, and consumes 1 liter of fuel. In the accelerated mode a car covers 1 kilometer in 1 minutes, but consumes 2 liters of fuel. The driving mode can be changed at any moment and any number of times.

Your task is to choose a car with minimum price such that Vasya can reach the cinema before the show starts, i.e. not later than in t minutes. Assume that all cars are completely fueled initially.

Input

The first line contains four positive integers n, k, s and t (1 ≤ n ≤ 2·10⁵, 1 ≤ k ≤ 2·10⁵, 2 ≤ s ≤ 10⁹, 1 ≤ t ≤ 2·10⁹) — the number of cars at the car rental service, the number of gas stations along the road, the length of the road and the time in which the film starts.

Each of the next n lines contains two positive integers c_i and v_i (1 ≤ c_i, v_i ≤ 10⁹) — the price of the i-th car and its fuel tank capacity.

The next line contains k distinct integers g₁, g₂, ..., g_k (1 ≤ g_i ≤ s - 1) — the positions of the gas stations on the road in arbitrary order.

Output

Print the minimum rent price of an appropriate car, i.e. such car that Vasya will be able to reach the cinema before the film starts (not later than in t minutes). If there is no appropriate car, print -1.

Examples

Input

3 1 8 10
10 8
5 7
11 9
3

Output

10

Input

2 2 10 18
10 4
20 6
5 3

Output

20

Note

In the first sample, Vasya can reach the cinema in time using the first or the third cars, but it would be cheaper to choose the first one. Its price is equal to 10, and the capacity of its fuel tank is 8. Then Vasya can drive to the first gas station in the accelerated mode in 3 minutes, spending 6 liters of fuel. After that he can full the tank and cover 2 kilometers in the normal mode in 4 minutes, spending 2 liters of fuel. Finally, he drives in the accelerated mode covering the remaining 3 kilometers in 3 minutes and spending 6 liters of fuel.

题意：给你n辆车的租金和油箱容量，和k个加油站的位置，电影院位于s处，需要在t时间到达，一公里匀速花费2分钟1升油，一公里加速花费1分钟2升油;求最小的花费是否可达;

思路：二分油箱大小，求最小的油箱大小使得可达，找大于等于这个数的最小花费，没有输出-1;ps：油居然不要钱;

#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define pi (4*atan(1.0))
#define eps 1e-14
const int N=1e6+,M=1e6+,inf=1e9+;
const ll INF=1e18+,mod=;
struct is
{
    int price,v;
}a[N];
int pos[N];
int n,k,s,t;
int check(int x)
{
    ll ans=;
    for(int i=;i<=k+;i++)
    {
        if(pos[i]-pos[i-]>x)
        return ;
        if(pos[i]-pos[i-]==x)
            ans+=x*;
        else if((pos[i]-pos[i-])* <=x)
            ans+=(pos[i]-pos[i-]);
        else
            ans+=(pos[i]-pos[i-])*-(x-pos[i]+pos[i-]);
    }
    if(ans<=t)
        return ;
    return ;
}
int main()
{
    scanf("%d%d%d%d",&n,&k,&s,&t);
    for(int i=;i<=n;i++)
        scanf("%d%d",&a[i].price,&a[i].v);
    for(int i=;i<=k;i++)
        scanf("%d",&pos[i]);
    sort(pos+,pos++k);
    pos[k+]=s;
    int st=,en=1e9,ans;
    while(st<=en)
    {
        int mid=(st+en)>>;
        if(check(mid))
        {
            ans=mid;
            en=mid-;
        }
        else
            st=mid+;
    }
    int out=inf;
    for(int i=;i<=n;i++)
    {
        if(a[i].v>=ans)
        {
            out=min(out,a[i].price);
        }
    }
    if(out==inf)
        printf("-1\n");
    else
        printf("%d\n",out);
    return ;
}