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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<iostream>
#define I(i,n)for(int i=0;i<n;i++)
long long M=1e9+7,n,a[2],s[100000],w[2][100001],e[2],l[2][100000],p;
int main(){
	std::cin>>n>>*a>>a[1];
	I(i,n)std::cin>>s[i];
	I(k,2){
		p=0;w[k][0]=1;
		I(i,n){
			while(s[i]-s[p]>=a[k]&&p<i-1)p++;
			l[k][i]=p;
		}
	}
	I(i,n){if(i){
		I(k,2)w[k][i]=(e[!k]<=l[k][i])*w[!k][l[k][i]];
		I(k,2)if(s[i]-s[i-1]<a[k])e[k]=i;else(w[k][i]+=w[k][i-1])%=M;
	}
	}
	std::cout<<(w[0][--n]+w[1][n])%M;
	return 0;
}