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 <algorithm>
using namespace std;
const int MAXN=1010000;
const int MOD=1e9+7;
long long n,a,b;
long long c[MAXN];
long long f[MAXN],s[MAXN];
int main()
{
//	freopen("test.in","r",stdin);
//	freopen("test.out","w",stdout);
    scanf("%lld%lld%lld",&n,&a,&b);
    if(a>b)swap(a,b);
    for(int i=1;i<=n;i++)
    {
        scanf("%lld",&c[i]);
        if(i>2&&c[i]-c[i-2]<a)
        {
            printf("0");
            return 0;
        }
    }	
    f[0]=s[0]=1;
    for(int i=1,l=0,r=0;i<=n;i++)
    {
        while(i>1&&c[i]-c[r+1]>=b)r++;
        if(l<=r)
        {	
            f[i]=s[r];
            if(l!=0)f[i]=(f[i]+MOD-s[l-1])%MOD;
        }
        s[i]=(s[i-1]+f[i])%MOD;
        if(i>1&&c[i]-c[i-1]<a)l=i-1;
    }
    long long ans=0;
    for(int i=n;i>=0;i--)
    {
        ans=(ans+f[i])%MOD;
        if(i<n&&a>c[i+1]-c[i])break;
    }
    printf("%lld",ans);
    return 0;
}