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 <cstdio>
#include <algorithm>

typedef long long LL;
const int Mod = 1000000007;
const int MN = 100005;

int N;
LL S[MN], A, B;
int b[MN], f[MN], g[MN];

int main() {
	scanf("%d%lld%lld", &N, &A, &B);
	if (A > B) std::swap(A, B);
	for (int i = 1; i <= N; ++i) scanf("%lld", &S[i]);
	f[1] = g[1] = 1;
	int j = 1;
	for (int i = 2; i <= N; ++i) {
		b[i] = b[i - 1] + (S[i] - S[i - 1] < A);
		if (S[i] - S[i - 1] >= A) f[i] = (f[i - 1] + g[i - 1]) % Mod;
		else if (i == 2 || S[i] - S[i - 2] >= A) f[i] = g[i - 1];
		while (j < i && S[i] - S[j] >= B) ++j;
		if (j == i) g[i] = (f[i - 1] + g[i - 1]) % Mod;
		else if (b[i - 1] - b[j] == 0) g[i] = f[j];
	}
	printf("%d\n", (f[N] + g[N]) % Mod);
	return 0;
}