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 mod 1000000007
#define maxn 100100
using namespace std;
typedef long long ll;
ll A[maxn],X,Y;
int n,fp,gp,tr[2][maxn],q[2][maxn*30],tp[2];
void add(int p,int x,int a){
	for(x++;x<=n+1;x+=x&-x)
		tr[p][x]=(tr[p][x]+a)%mod,q[p][++tp[p]]=x;
}
int qry(int p,int x){
	int ans=0;
	for(x++;x;x-=x&-x)
		ans=(ans+tr[p][x])%mod;
	return ans;
}
void clear(int p){
	while(tp[p])
		tr[p][q[p][tp[p]--]]=0;
}
int main(){
	scanf("%d%lld%lld",&n,&X,&Y);
	for(int i=1;i<=n;++i)
		scanf("%lld",&A[i]);
	A[0]=(ll)-3e18;
	add(0,0,1),add(1,0,1);
	for(int i=2;i<=n;++i){
		while(fp+1<i&&A[i]-A[fp+1]>=X)fp++;
		while(gp+1<i&&A[i]-A[gp+1]>=Y)gp++;
		int p=qry(1,fp),q=qry(0,gp);
		if(A[i]-A[i-1]<X)clear(0);
		if(A[i]-A[i-1]<Y)clear(1);
		add(0,i-1,p),add(1,i-1,q);
	}
	printf("%d",(qry(0,n-1)+qry(1,n-1))%mod);
}