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>
#include <fstream>
#include <typeinfo>
#include <vector>
#include <stack>
#include <cmath>
#include <set>
#include <map>
#include <string>
#include <algorithm>
#include <cstdio>
#include <queue>
#include <iomanip>
#include <cctype>
#define syosu(x) fixed<<setprecision(x)
using namespace std;
typedef long long ll;
typedef pair<int,int> P;
typedef pair<double,double> pdd;
typedef pair<ll,ll> pll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<double> vd;
typedef vector<vd> vvd;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<char> vc;
typedef vector<vc> vvc;
typedef vector<string> vs;
typedef vector<bool> vb;
typedef vector<vb> vvb;
typedef vector<P> vp;
typedef vector<vp> vvp;
typedef vector<pll> vpll;
typedef pair<int,P> pip;
typedef vector<pip> vip;
const int inf=1<<30;
const ll INF=1ll<<52;
const double pi=acos(-1);
const double eps=1e-8;
const ll mod=1e9+7;
const vi emp;
const int dx[4]={0,1,0,-1},dy[4]={1,0,-1,-0};
const int DX[8]={-1,-1,-1,0,0,1,1,1},DY[8]={1,0,-1,1,-1,1,0,-1};

ll n,a,b;
vl s;

int main(){
	cin>>n>>a>>b;
	s=vl(n);
	for(int i=0;i<n;i++) cin>>s[i];
	// 0:X 1:Y
	vvl dp(n,vl(2));
	int x=0,y=0;
	dp[0][0]++;
	dp[0][1]++;
	for(int i=1;i<n;i++){
		auto it=upper_bound(s.begin(),s.end(),s[i]-a);
		auto jt=upper_bound(s.begin(),s.end(),s[i]-b);
		if(it==s.begin()+i) dp[i][0]=(dp[i-1][0]+dp[i-1][1])%mod;
		else if(y<=it-s.begin()) dp[i][0]=dp[it-s.begin()][1];
		if(jt==s.begin()+i) dp[i][1]=(dp[i-1][0]+dp[i-1][1])%mod;
		else if(x<=jt-s.begin()) dp[i][1]=dp[jt-s.begin()][0];
		if(s[i]-s[i-1]<a) x=i;
		if(s[i]-s[i-1]<b) y=i;
	}
	cout<<(dp[n-1][0]+dp[n-1][1])%mod<<endl;
}