Problem: 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.

Examples

Input

5 3 7
1
3
6
9
12


Output

5


Input

7 5 3
0
2
4
7
8
11
15


Output

4


Input

8 2 9
3
4
5
13
15
22
26
32


Output

13


Input

3 3 4
5
6
7


Output

0

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;
#define MAXN	100005
#define P	1000000007
long long f[MAXN], sum[MAXN];
long long a, b, A[MAXN];
bool tmp[MAXN];
int pre[MAXN];
int main() {
	int n;
	scanf("%d%lld%lld", &n, &a, &b);
	for (int i = 1; i <= n; i++)
		scanf("%lld", &A[i]);
	if (a < b) swap(a, b);
	for (int i = 3; i <= n; i++)
		if (A[i] - A[i - 2] < b) {
			printf("0\n");
			return 0;
		}
	int now = 0;
	for (int i = 2; i <= n; i++) {
		tmp[i] = A[i] - A[i - 1] < b;
		pre[i] = now;
		if (tmp[i]) now = i - 1;
	}
	A[n + 1] = 3e18;
	pre[n + 1] = now;
	now = 0;
	f[0] = sum[0] = 1;
	for (int i = 1; i <= n + 1; i++) {
		while (A[i] - A[now + 1] >= a) now++;
		if (now >= pre[i]) {
			if (pre[i] >= 1) f[i] = (sum[now] - sum[pre[i] - 1]) % P;
			else f[i] = sum[now] % P;
		} else f[i] = 0;
		sum[i] = (f[i] + sum[i - 1]) % P;
	}
	printf("%lld\n", (f[n + 1] + P) % P);
	return 0;
}