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;

typedef long long LL;
#define N 120000
#define INF 0x3f3f3f3f3f3f3f3fLL

const LL mod=1000000007;
LL n,x,y,a[N],f[N];

int main(){
	scanf("%lld%lld%lld",&n,&x,&y);
	if (x>y) swap(x,y);
	for (LL i=1;i<=n;++i) scanf("%lld",a+i);
	for (LL i=3;i<=n;++i)
		if (a[i]-a[i-2]<x){puts("0"); return 0;}
	f[0]=1; a[0]=-INF; a[n+1]=INF;
	for (LL i=1,j=0,k=0;i<=n+1;++i){
		for (;k+1<i&&a[i]-a[k+1]>=y;++k);
		if (j<=k) f[i]=(f[k]-(j?f[j-1]:0))%mod;
		f[i]=(f[i-1]+f[i])%mod;
		if (i>1&&a[i]-a[i-1]<x) j=i-1;
	}
	printf("%lld\n",(f[n+1]-f[n]+mod*2)%mod);
	
	return 0;
}