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 <cstdio>
#include <cctype>
#include <algorithm>
#define repu(i,x,y) for (int i=x; i<=y; ++i)
using namespace std;

typedef long long LL;
const int p=1000000007;
int n,f[100100],g[100100];
LL a[100100],x,y;

LL getLL()
{
    char ch;
    while (!isdigit(ch=getchar()));
    LL x=ch-'0';
    for (; isdigit(ch=getchar()); x=x*10+ch-'0');
    return x;
}

int main()
{
    scanf("%d%lld%lld",&n,&x,&y);
    repu(i,1,n)
        a[i]=getLL();
    f[0]=g[0]=1,f[1]=g[1]=p-1,a[0]=-1LL<<61,a[n+1]=1LL<<61;
    for (int i=0,l1=1,r1=1,l2=1,r2=1; i<n; ++i)
    {
        for (l1=max(l1,i+1); a[l1+1]-a[i]<x; ++l1);
        for (r1=max(r1,i+1); r1<n && a[r1+1]-a[r1]>=y; ++r1);
        for (l2=max(l2,i+1); a[l2+1]-a[i]<y; ++l2);
        for (r2=max(r2,i+1); r2<n && a[r2+1]-a[r2]>=x; ++r2);
        if (l1<=r1)
            (g[l1]+=f[i])%=p,(g[r1+1]+=p-f[i])%=p;
        if (l2<=r2)
            (f[l2]+=g[i])%=p,(f[r2+1]+=p-g[i])%=p;
        (f[i+1]+=f[i])%=p,(g[i+1]+=g[i])%=p;
    }
    printf("%d\n",(f[n]+g[n])%p);
    return 0;
}