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<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
#define N 100005
#define mod 1000000007
using namespace std;
typedef long long LL;
inline LL read()
{
	char c=getchar(); LL num=0,f=1;
	while (c<'0'||c>'9') { if (c=='-') f=-1; c=getchar(); }
	while (c<='9'&&c>='0') { num=num*10+c-'0'; c=getchar(); }
	return num*f;
}
LL n,A,B,s[N],f[N],g[N],ans;
int main()
{
	n=read(); A=read(); B=read(); if (A>B) swap(A,B);
	for (int i=1;i<=n;i++) s[i]=read();	
	for (int i=3;i<=n;i++) if (s[i]-s[i-2]<A) { printf("0"); return 0; }
	f[0]=g[0]=1; int l=0,r=0;
	for (int i=1;i<=n;i++)
	{
		while (r<i-1&&s[i]-s[r+1]>=B) r++;
		if (l<=r) f[i]=(g[r]-(l?g[l-1]:0)+mod)%mod;
		g[i]=(g[i-1]+f[i])%mod;
		if (i>1&&s[i]-s[i-1]<A) l=i-1;
	}
	for (int i=n;i>=0;i--)
	{
		ans=(ans+f[i])%mod;
		if (i<n&&s[i+1]-s[i]<A) break;
	}
	cout<<ans;
	return 0;
}