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 LL long long

const int maxn=1e5+10;
const int mo=1e9+7;

int n,dp[maxn],pre[maxn];
LL A,B,S[maxn];

int main()
{
#ifdef h10
	freopen("C.in","r",stdin);
	freopen("C.out","w",stdout);
#endif
	int i,L=0,R=0;
	scanf("%d%lld%lld",&n,&A,&B);
	if (A>B) swap(A,B);
	for (i=1;i<=n;i++)
		scanf("%lld",&S[i]);
	for (i=3;i<=n;i++)
		if (S[i]-S[i-2]<A) {puts("0"); return 0;}
	S[0]=S[1]-B;
	dp[0]=pre[0]=1;
	for (i=1;i<=n;i++)
	{
		while (S[i]-S[R+1]>=B) R++;
		if (L<=R) dp[i]=(pre[R]+mo-(L?pre[L-1]:0))%mo;
		pre[i]=(pre[i-1]+dp[i])%mo;
		if (S[i]-S[i-1]<A) L=i-1;
	}
	printf("%d\n",(pre[n]+mo-(L?pre[L-1]:0))%mo);
}