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;
int n, L, R, p = 1000000007;
long long a[100020], A, B;
int f[100020];
int s[100020];
int main() {
	scanf("%d%lld%lld", &n, &A, &B);
	if (A > B) {
		swap(A, B);
	}
	for (int i = 1; i <= n; i++) {
		scanf("%lld", &a[i]);
	}
	for (int i = 3; i <= n; i++) {
		if (a[i] - a[i - 2] < A) {
			printf("0\n");
			return 0;
		}
	}
	a[0] = a[1] - B;
	s[1] = f[0] = 1;
	for (int i = 1; i <= n; i++) {
		while (a[i] - a[R] >= B) {
			R++;
		}
		f[i] = (s[R] - s[L] + p) % p;
		s[i + 1] = (s[i] + f[i]) % p;
		if (i > 0 && a[i] - a[i - 1] < A) {
			L = i - 1;
			R = max(R, L);
		}
	}
	printf("%d\n", (s[n + 1] - s[L] + p) % p);
	return 0;
}