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>
using namespace std;
 
#define iter(i, n) for (int i = 1; i <= n; ++i)
#define forw(i, a, b) for (int i = a; i <= b; ++i)
#define NR 101000
 
const int mod = 1000000007;
 
int n, f[NR], sum[NR], L[NR], R[NR];
long long a[NR], dA, dB;
 
int main() {
	scanf("%d%lld%lld", &n, &dA, &dB);
	if (dA > dB) swap(dA, dB);
	iter(i, n) scanf("%lld", &a[i]);
 
	int p = 0;
	forw(i, 2, n) {
		if (i > 2 && a[i] - a[i - 2] < dA) {
			printf("0\n");
			return 0;
		}
 
		L[i] = (a[i] - a[i - 1] >= dA) ? L[i - 1] : i - 1;
		for (; a[i] - a[p + 1] >= dB; ++p);
		R[i] = p;
	}
 
	f[0] = sum[0] = 1;
	L[1] = R[1] = 0;
 
	iter(i, n) {
		if (L[i-1] <= R[i]) f[i] = (sum[R[i]] - (L[i - 1] > 0 ? sum[L[i - 1] - 1] : 0) + mod) % mod;
		sum[i] = (sum[i - 1] + f[i]) % mod;
//printf("%d %d %d\n", f[i], L[i - 1], R[i]);
	}
 
	printf("%d\n", (sum[n] - (L[n] > 0 ? sum[L[n] - 1] : 0) + mod) % mod);
	return 0;
}