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>
using namespace std;
const int N=100005;
const int mod=1000000007;
int n,i,j,l,r;
int f[N],p[N];
long long s[N],a,b;
int main()
{
	scanf("%d",&n);
	scanf("%lld%lld",&a,&b);
	for (i=1;i<=n;i++)
		scanf("%lld",&s[i]);
	if (a>b)
		a^=b^=a^=b;
	for (i=3;i<=n;i++)
		if (s[i]-s[i-2]<a)
		{
			printf("%d\n",0);
			return 0;
		}
	f[0]=1;
	p[0]=1;
	for (i=1;i<=n;i++)
	{
		while (r<i-1&&s[i]-s[r+1]>=b)
			r++;
		if (l<=r)
			f[i]=(p[r]+mod-(l?p[l-1]:0))%mod;
		p[i]=(p[i-1]+f[i])%mod;
		if (i>1&&s[i]-s[i-1]<a)
			l=i-1;
	}
	for (i=n;i>=1;i--)
		if (i<n&&s[i+1]-s[i]<a)
			break;
	printf("%d\n",(p[n]+mod-(i?p[i-1]:0))%mod);
	return 0;
}