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: Time Limit Exceeded)

#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
using namespace std;
int n;
long long a,b;
long long e[100010];
int lsta[100010],lstb[100010];
long long dp1[100010],dp2[100010];
const long long md=1e9+7;
void pls(long long& x,long long y)
{
	x+=y;
	if(x>md)x-=md;
}
int main()
{
	scanf("%d%lld%lld",&n,&a,&b);
	for(int i=1;i<=n;i++)
	{
		scanf("%lld",e+i);
	}
	for(int i=2;i<=n;i++)
	{
		for(lsta[i]=lsta[i-1];e[lsta[i]+1]+a<=e[i];lsta[i]++);
		for(lstb[i]=lstb[i-1];e[lstb[i]+1]+b<=e[i];lstb[i]++);
	}
	dp1[0]=dp2[0]=1;
	for(int i=2;i<=n;i++)
	{
		long long ax=dp2[min(i-2,lsta[i])],ay=dp1[min(i-2,lstb[i])];
		if(lsta[i]!=i-1)memset(dp1,0LL,sizeof(dp1));
		if(lstb[i]!=i-1)memset(dp2,0LL,sizeof(dp2));
		pls(dp1[i-1],ax+dp1[i-2]);
		pls(dp2[i-1],ay+dp2[i-2]);
	}
	long long ans=(dp1[n-1]+dp2[n-1])%md;
	printf("%lld",ans);
	return 0;
}