Problem:
Score : 1100 points

Problem Statement

There is a set consisting of N distinct integers. The i-th smallest element in this set is S_i. We want to divide this set into two sets, X and Y, such that:

The absolute difference of any two distinct elements in X is A or greater.

The absolute difference of any two distinct elements in Y is B or greater.

How many ways are there to perform such division, modulo 10^9 + 7? Note that one of X and Y may be empty.

Constraints

All input values are integers.

1 ≦ N ≦ 10^5

1 ≦ A , B ≦ 10^{18}

0 ≦ S_i ≦ 10^{18}(1 ≦ i ≦ N)

S_i < S_{i+1}(1 ≦ i ≦ N - 1)

Input

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

N A B
S_1
:
S_N

Output

Print the number of the different divisions under the conditions, modulo 10^9 + 7.

Sample Input 1

5 3 7
1
3
6
9
12

Sample Output 1

5

There are five ways to perform division:

X={1,6,9,12}, Y={3}

X={1,6,9}, Y={3,12}

X={3,6,9,12}, Y={1}

X={3,6,9}, Y={1,12}

X={3,6,12}, Y={1,9}

Sample Input 2

7 5 3
0
2
4
7
8
11
15

Sample Output 2

4

Sample Input 3

8 2 9
3
4
5
13
15
22
26
32

Sample Output 3

13

Sample Input 4

3 3 4
5
6
7

Sample Output 4

0

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.Arrays;
import java.util.Scanner;

class BIT{
    int N;
    long[] data;
    long inf = (long)1e9+7;
    
    public BIT(int n){
        N = n;
        data = new long[N+1];
        Arrays.fill(data,0);
    }

    public void add(int pos,long dat){
        for(int x = pos;x<=N; x += x&-x)data[x] = (data[x]+dat)%inf;
    }

    public long getSum(int pos){
        if(pos==0)return 0;
        long res = 0;
        for(int x = pos; x>0;x-=x&-x)res=(res+data[x])%inf;
        return res;
    }

}



class Main{

    static long A,B;
    static int N;
    static long[] S;
    static int findIndex(long s){
        int left=0;
        int right=N+1;
        while(right-left>1){
            int center = (left+right)/2;
            if(s-S[center] >=B)left=center;
            else right=center;
        }
        return left;
    }

    public static void main(String[] args){
        Scanner scan = new Scanner(System.in);
        N = scan.nextInt();
        A = scan.nextLong();
        B = scan.nextLong();
        S = new long[N+1];
        S[0]=-B;
        for(int i=0;i<N;++i)S[i+1] = scan.nextLong();
        if(A>B){
            long a = A;
            A=B;
            B=a;
        }
        for(int i=1;i+2<N+1;++i)if(S[i+2]-S[i] < A){
                System.out.println(0);
                return;
        }
        long mod = (long)1e9+7;
        //1-index
        BIT bit = new BIT(N+1);
        bit.add(1, 1);
        bit.add(2,1);
        int leftindex = 0;
        for(int i=2;i<=N;++i){
            long delta = S[i]-S[i-1];
            if(delta < A){
                bit.add(i+1, (bit.getSum(findIndex(S[i])+1) - bit.getSum(leftindex)+mod)%mod);
                leftindex = i-1;
            }
            else if(delta < B){
                bit.add(i+1, (bit.getSum(findIndex(S[i])+1) - bit.getSum(leftindex)+mod)%mod);
            }
            else bit.add(i+1, (bit.getSum(i+1) - bit.getSum(leftindex) + mod)%mod);
        }
        System.out.println((bit.getSum(N+1) - bit.getSum(leftindex)+mod)%mod);
    }
}