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>
using namespace std;
#define N 1111116
#define mod 1000000007

int n,ta,tb;
long long a,b,s[N],f[N],g[N],cnta,cntb;

long long read(){
	long long x=0,f=1;char ch=getchar();
	for (;!isdigit(ch);ch=getchar()) if (ch=='-')  f=-f;
	for (;isdigit(ch);ch=getchar()) x=x*10+ch-'0';
	return x*f;
}

int main(){
	n=read();a=read();b=read();
	for (int i=1;i<=n;i++) s[i]=read();
	s[0]=-1ll<<60;f[0]=g[0]=1;
	ta=tb=1,cnta=cntb=1;
	for (int i=1;i<n;i++){
		while (ta<i&&s[i+1]-s[ta]>=b)
			cnta=(cnta+f[ta++])%mod;
		g[i]=cnta;
		if (s[i+1]-s[i]<a) ta=i,cnta=0;
		while (tb<i&&s[i+1]-s[tb]>=a)
			cntb=(cntb+g[tb++])%mod;
		f[i]=cntb;
		if (s[i+1]-s[i]<b) tb=i,cntb=0;
	}
	while (ta<n) cnta=(cnta+f[ta++])%mod;
	while (tb<n) cntb=(cntb+g[tb++])%mod;
	printf("%lld\n",(cnta+cntb)%mod);
	return 0;
}