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: Runtime Error)

#include <cstdio>
#include <algorithm>
using namespace std;
const int MAXN=1010000;
const int MOD=1e9+7;
int n,a,b;
int c[MAXN];
int f[MAXN],s[MAXN];
int main()
{
	//freopen("test.in","r",stdin);
	//freopen("test.out","w",stdout);
	scanf("%d%d%d",&n,&a,&b);
	if(a>b)swap(a,b);
	for(int i=1;i<=n;i++)
	{
		scanf("%d",&c[i]);
		if(i>2&&c[i]-c[i-2]<a)
		{
			printf("0");
			return 0;
		}
	}	
	f[0]=s[0]=1;
	for(int i=1,l=0,r=0;i<=n;i++)
	{
		while(i>1&&c[i]-c[r+1]>=b)r++;
		f[i]=s[r];
		if(l!=0)f[i]=(f[i]+MOD-s[l-1])%MOD;
		s[i]=(s[i-1]+f[i])%MOD;
		if(i>1&&c[i]-c[i-1]<a)l=i-1;
	}
	int ans=0;
	for(int i=n;i>=0;i--)
	{
		ans=(ans+f[i])%MOD;
		if(i<n&&a>c[i+1]-c[i])break;
	}
	printf("%d",ans);
	return 0;
}