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<cstdlib>
#include<cstring>
#include<algorithm>
using namespace std;

typedef long long LL;

const int N=100005;
const int MOD=1000000007;

int n,f[N],g[N];
LL a,b,s[N];

int main()
{
    scanf("%d%lld%lld",&n,&a,&b);
    if (a>b) swap(a,b);
    for (int i=1;i<=n;i++) scanf("%lld",&s[i]);
    sort(s+1,s+n+1);
    for (int i=3;i<=n;i++) if (s[i]-s[i-2]<a) {puts("0");return 0;}
    f[0]=g[0]=1;int p=0,lim=0;
    for (int i=1;i<=n;i++)
    {
        while (p<i&&s[i]-s[p+1]>=b) p++;
        if (lim<=p) f[i]=(g[p]+MOD-(lim?g[lim-1]:0))%MOD;
        g[i]=(g[i-1]+f[i])%MOD;
        if (i>1&&s[i]-s[i-1]<a) lim=i-1;
    }
    int ans=0;
    for (int i=n;i>=0;i--)
    {
        (ans+=f[i])%=MOD;
        if (i<n&&s[i+1]-s[i]<a) break;
    }
    printf("%d",ans);
    return 0;
}