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 int long long
#define mod 1000000007
#define N 300010
using namespace std;

inline int read()
{
	int x=0,f=1; char ch=getchar();
	while(ch<'0'||ch>'9'){if(ch=='-')f=-1; ch=getchar();}
	while(ch>='0'&&ch<='9'){x=x*10+ch-'0'; ch=getchar();}
	return x*f;
}
int F[N],S[N],n,A,B;
signed main()
{
	int L=0,R=0;
	scanf("%lld%lld%lld",&n,&A,&B);
	if (A>B) swap(A,B);
	for (int i=1;i<=n;i++)
		scanf("%lld",&S[i]);
	for (int i=3;i<=n;i++)
		if (S[i]-S[i-2]<A) {puts("0"); return 0;}
	S[0]=S[1]-B; F[0]=1;
	for (int i=1;i<=n;i++)
	{
		while (S[i]-S[R+1]>=B&&R+1<=i) R++;
		if (L<=R) F[i]=(F[R]+mod-(L?F[L-1]:0))%mod;
		F[i]=(F[i-1]+F[i])%mod;
		if (S[i]-S[i-1]<A) L=i-1;
	}
	printf("%lld\n",(F[n]+mod-(L?F[L-1]:0))%mod);
}