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>
#define LL long long
#define mod 1000000007
using namespace std;

LL N,A,B,a[100010],cl[100010],dp[100010],s[100010];

int main(){
    ios::sync_with_stdio(0);
    cin.tie(0);

    cin >> N >> A >> B;
    if (A>B) swap(A,B);
    LL i;
    for (i=1; i<=N; i++) cin >> a[i];

    for (i=1; i<=N-2; i++)
        if (a[i+2]-a[i]<A){
            cout << 0 << "\n";
            return 0;
        }

    a[0]=-B;
    cl[N]=cl[N-1]=N+1;
    for (i=N-2; i>=0; i--){
        cl[i]=cl[i+1];
        if (a[i+2]-a[i+1]<A) cl[i]=i+1;
    }

    LL l=N+1;
    for (i=N; i>=0; i--){
        while (a[l-1]-a[i]>=B) l--;
        if (l==N+1){
            if (cl[i]==N+1) dp[i]=1;
            else dp[i]=0;
        }
        else{
            if (cl[i]==N+1) dp[i]=(1+s[l])%mod;
            else{
                if (l>cl[i]+1) dp[i]=0;
                else dp[i]=(s[l]-s[cl[i]+2]+mod)%mod;
            }
        }

        s[i]=(s[i+1]+dp[i])%mod;
    }

    cout << (dp[0]+mod)%mod << "\n";
    return 0;
}