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
using namespace std;
const LL inf=3000000000000000000ll;
const int mo=1000000007;
LL A,B,w[100005]; int f[100005],g[100005],a[100005],b[100005],n,p,q;
int main(){
	scanf("%d%lld%lld",&n,&A,&B);
	for (int i=1;i<=n;++i) scanf("%lld",&w[i]);
	w[0]=-inf; w[n+1]=inf;
	for (int i=1;i<=n;++i){
		if (w[i]-w[i-1]>=A) a[i]=a[i-1]; else a[i]=i;
		if (w[i]-w[i-1]>=B) b[i]=b[i-1]; else b[i]=i;
	}
	f[0]=g[0]=1;
	for (int i=1;i<=n;++i){
		while (p<i&&w[p]+A<=w[i+1]) ++p;
		while (q<i&&w[q]+B<=w[i+1]) ++q;
		f[i]=q>=a[i]?(g[q-1]-(a[i]>1?g[a[i]-2]:0))%mo:0;
		g[i]=p>=b[i]?(f[p-1]-(b[i]>1?f[b[i]-2]:0))%mo:0;
		(f[i]+=f[i-1])%=mo;
		(g[i]+=g[i-1])%=mo;
	}
	printf("%d\n",((1ll*f[n]-f[n-1]+g[n]-g[n-1])%mo+mo)%mo);
	return 0;
}