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>

const int N=100005,mo=1000000007;
int f0[N],f1[N];
long long a[N],A,B;

int main(){
	int n,l0=0,l1=0,r0=0,r1=0,s0=0,s1=0;
	scanf("%d%lld%lld\n%lld",&n,&A,&B,&a[1]);
	a[0]=-1e18;f0[0]=f1[0]=1;
	for (int i=1;i<n;i++){
		scanf("%lld",&a[i+1]);
		for (;l0<i && a[i+1]-a[l0]>=B;l0++) (s0+=f0[l0])%=mo;
		for (;l1<i && a[i+1]-a[l1]>=A;l1++) (s1+=f1[l1])%=mo;
		f0[i]=s1;f1[i]=s0;
		if (a[i+1]-a[i]<A) for (;r0<i;f0[r0++]=0) if (r0<l0) (s0-=f0[r0])%=mo;
		if (a[i+1]-a[i]<B) for (;r1<i;f1[r1++]=0) if (r1<l1) (s1-=f1[r1])%=mo;
	}
	int ans=0;
	for (int i=r0;i<n;i++) (ans+=f0[i])%=mo;
	for (int i=r1;i<n;i++) (ans+=f1[i])%=mo;
	printf("%d\n",(ans+mo)%mo);
}