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>

const int N = 1e5 + 9, P = 1e9 + 7;

typedef long long ll;
int n, ans;
ll a, b, s[N], sum[N], f[N];
typedef long long ll;

int main () {
	scanf("%d%lld%lld", &n, &a, &b); if (a > b) a ^= b ^= a ^= b;
	s[0] = -1e18; f[0] = sum[0] = 1;
	for (int i = 1, j = 0, k = -1; i <= n; ++i) {
		scanf("%lld", &s[i]);
		if (i > 2 && s[i] - s[i - 2] < a) return puts("0"), 0;
		while (s[i] - s[j] >= b) ++j; --j;
		if (j > k) f[i] = (sum[j] - (k == -1 ? 0 : sum[k])) % P;
		if (s[i] - s[i - 1] < a) k = i - 2;
		sum[i] = (sum[i - 1] + f[i]) % P;
	}
	for (int i = n; ~i; --i) {
		ans = (ans + f[i]) % P;
		if (i < n && s[i + 1] - s[i] < a) break ;
	}
	printf("%d\n", (ans + P) % P);
	return 0;
}