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<bits/stdc++.h>
using namespace std;
typedef long long giant;
inline char nchar() {
	static const int bufl=1<<20;
	static char buf[bufl],*a=NULL,*b=NULL;
	return a==b && (b=(a=buf)+fread(buf,1,bufl,stdin),a==b)?EOF:*a++;
}
template<class T> inline T read() {
	T x=0,f=1;
	char c=nchar();
	for (;!isdigit(c);c=nchar()) if (c=='-') f=-1;
	for (;isdigit(c);c=nchar()) x=x*10+c-'0';
	return x*f;
}
const int maxn=1e5+1;
const int q=1e9+7;
const giant inf=2e18;
inline int Plus(int x,int y) {return (x+=y)>=q?x-q:x;}
inline void Pe(int &x,int y) {x=Plus(x,y);}
int n,f[maxn][2];
giant lim[2],a[maxn];
namespace sgt {
	const int maxp=8e6;
	struct node {
		int l,r,s;
	} t[maxp];
	int tot=0;
	inline void newnode(int &x) {
		int y=x;
		t[x=++tot]=t[y];
	}
	void modify(int &x,int l,int r,int p,int d) {
		newnode(x);
		if (l==r) {t[x].s=d;return;}
		int mid=l+r>>1;
		p<=mid?modify(t[x].l,l,mid,p,d):modify(t[x].r,mid+1,r,p,d);
		t[x].s=Plus(t[t[x].l].s,t[t[x].r].s);
	}
	inline void modify(int &x,int p,int d) {
		modify(x,0,n,p,d);
	}
	int sum(int x,int L,int R,int l,int r) {
		if (!x) return 0;
		if (L==l && R==r) return t[x].s;
		int mid=L+R>>1;
		if (r<=mid) return sum(t[x].l,L,mid,l,r);
		if (l>mid) return sum(t[x].r,mid+1,R,l,r);
		return Plus(sum(t[x].l,L,mid,l,mid),sum(t[x].r,mid+1,R,mid+1,r));
	}
	inline int sum(int x,int l,int r) {
		return sum(x,0,n,l,r);
	}
}
int main() {
	n=read<int>(),lim[0]=read<giant>(),lim[1]=read<giant>();
	a[0]=-inf,generate(a+1,a+n+1,read<giant>);
	for (int i=0;i<2;++i) sgt::modify(f[1][i],0,1);
	for (int x=2;x<=n;++x) for (int c=0;c<2;++c) {
		if (a[x]-a[x-1]>=lim[c]) f[x][c]=f[x-1][c];
		int j=upper_bound(a,a+x,a[x]-lim[c])-a-1;
		sgt::modify(f[x][c],x-1,sgt::sum(f[x-1][c^1],0,j));
	}
	int ans=Plus(sgt::sum(f[n][0],0,n-1),sgt::sum(f[n][1],0,n-1));
	cout<<ans<<endl;
	return 0;
}