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: Wrong Answer)

/*
	无记忆化爆搜
	专业爆搜三十年
*/ 
#include <iostream>
#include <cstdio>
#include <cmath>
#include <vector>
#include <cstring>
#include <stack>
#include <queue>
#include <algorithm>
#include <set>
#include <map>
#define pb push_back
#define mp make_pair
#define INF 9999999
#define LINF 9999999999999999
#define SINF "%"
#define uint unsigned int
#define msn(a,v) memset(a,v,sizeof(a))
#define ms(a) msn(a,0)
#define NONE -1
#define ll long long
#define ull unsigned ll
#define uchar unsigned char
#define sint short int
#define usint unsigned sint
#define xsize(a) sizeof(a)/1024/1024
#define fr(aaaaa,bbbbb) for(aaaaa = 1;aaaaa <= bbbbb;aaaaa++)
#define frr(aaaaa,bbbbb,ccccc) for(aaaaa = ccccc;aaaaa <= bbbbb;aaaaa++)
using namespace std;
#define MAXN 100100
#define MOD 1000000007

ll n,a,b;
ll data[MAXN];

//		位置   X中最后一个数 
ll dfs(int pos,ll lastx,ll lasty){
	if(pos == n+1) return 1;
	ll ans = 0;
	if(data[pos] - lastx >= a) ans += dfs(pos+1,data[pos],lasty);
	if(data[pos] - lasty >= b) ans += dfs(pos+1,lastx,data[pos]);
	return ans;
}

int main(){
	//freopen("C.txt","r",stdin);
	
	cin >> n >> a >> b;
	if(a > b) swap(a,b);
	for(int i = 1;i <= n;i++)
		cin >> data[i];
	
	cout << dfs(1,-233,-233) << endl;
	
	return 0;
}