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<bits/stdc++.h>
#define ll long long
#define mod 1000000007
#define N 100009
using namespace std;

int n,sa[N],sb[N]; ll A,B,p[N]; bool va[N],vb[N];
int main(){
	scanf("%d%lld%lld",&n,&A,&B);
	int i,j,fa,fb,ka,kb,x,y;
	for (i=1; i<=n; i++) scanf("%lld",&p[i]);
	memset(va,1,sizeof(va));
	memset(vb,1,sizeof(vb));
	for (i=2,fa=fb=ka=kb=1; i<=n; i++){
		for (; ka+1<i && p[i]-p[ka]>=A; ka++);
		for (; kb+1<i && p[i]-p[kb]>=B; kb++);
		x=sb[ka-1]+fb; y=sa[kb-1]+fa;
		if (p[i]-p[i-1]<A){
			fa=0;
			for (j=i-2; j && va[j]; j--){
				va[j]=0; sa[j]=0;
			}
		}
		if (p[i]-p[i-1]<B){
			fb=0;
			for (j=i-2; j && vb[j]; j--){
				vb[j]=0; sb[j]=0;
			}
		}
		sa[i-1]=(sa[i-2]+x)%mod; sb[i-1]=(sb[i-2]+y)%mod;
	}
	printf("%d\n",(sa[n-1]+sb[n-1]+fa+fb)%mod);
	return 0;
}